LMFDB - Embedded newform 983.2.c.a.2.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(2,983)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(982))

chi = DirichletCharacter(H, H._module([674]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("983.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.c (of order $491$, degree $490$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$39690$
Relative dimension:	$81$ over $\Q(\zeta_{491})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{491}]$

Embedding invariants

Embedding label			2.6
Character	$\chi$	$=$	983.2
Dual form			983.2.c.a.492.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.805572 + 2.40575i) q^{2} +(-0.153383 - 0.0861729i) q^{3} +(-3.54199 - 2.67165i) q^{4} +(-0.680394 + 1.02626i) q^{5} +(0.330872 - 0.299584i) q^{6} +(1.03475 - 2.28334i) q^{7} +(5.09698 - 3.49786i) q^{8} +(-1.54443 - 2.53574i) q^{9} +O(q^{10})$	\(q+(-0.805572 + 2.40575i) q^{2} +(-0.153383 - 0.0861729i) q^{3} +(-3.54199 - 2.67165i) q^{4} +(-0.680394 + 1.02626i) q^{5} +(0.330872 - 0.299584i) q^{6} +(1.03475 - 2.28334i) q^{7} +(5.09698 - 3.49786i) q^{8} +(-1.54443 - 2.53574i) q^{9} +(-1.92082 - 2.46358i) q^{10} +(-2.29938 - 0.147324i) q^{11} +(0.313059 + 0.715010i) q^{12} +(3.73418 + 4.31455i) q^{13} +(4.65958 + 4.32875i) q^{14} +(0.192797 - 0.0987793i) q^{15} +(1.87110 + 6.54813i) q^{16} +(0.975206 - 0.430705i) q^{17} +(7.34452 - 1.67281i) q^{18} +(0.853792 + 0.652610i) q^{19} +(5.15175 - 1.81722i) q^{20} +(-0.355475 + 0.261058i) q^{21} +(2.20674 - 5.41307i) q^{22} +(-0.310345 - 2.92870i) q^{23} +(-1.08321 + 0.0972912i) q^{24} +(1.35635 + 3.20899i) q^{25} +(-13.3879 + 5.50785i) q^{26} +(0.0369481 + 1.04950i) q^{27} +(-9.76535 + 5.32307i) q^{28} +(-2.97208 + 4.30127i) q^{29} +(0.0823270 + 0.543395i) q^{30} +(4.90984 + 7.30375i) q^{31} +(-4.90937 - 0.220030i) q^{32} +(0.339992 + 0.220742i) q^{33} +(0.250572 + 2.69307i) q^{34} +(1.63926 + 2.61549i) q^{35} +(-1.30423 + 13.1077i) q^{36} +(1.22224 - 0.303170i) q^{37} +(-2.25781 + 1.52829i) q^{38} +(-0.200964 - 0.983565i) q^{39} +(0.121751 + 7.61073i) q^{40} +(-8.48523 - 0.762121i) q^{41} +(-0.341681 - 1.06549i) q^{42} +(3.51714 + 4.82143i) q^{43} +(7.75080 + 6.66496i) q^{44} +(3.65314 + 0.140314i) q^{45} +(7.29574 + 1.61267i) q^{46} +(1.40364 + 4.68444i) q^{47} +(0.277276 - 1.16561i) q^{48} +(0.471797 + 0.538126i) q^{49} +(-8.81267 + 0.677972i) q^{50} +(-0.186695 - 0.0179734i) q^{51} +(-1.69949 - 25.2585i) q^{52} +(1.18501 - 1.08683i) q^{53} +(-2.55460 - 0.756559i) q^{54} +(1.71568 - 2.25952i) q^{55} +(-2.71269 - 15.2575i) q^{56} +(-0.0747202 - 0.173673i) q^{57} +(-7.95357 - 10.6151i) q^{58} +(8.33995 + 0.641605i) q^{59} +(-0.946788 - 0.165210i) q^{60} +(1.43961 + 1.22200i) q^{61} +(-21.5263 + 5.92817i) q^{62} +(-7.38805 + 0.902607i) q^{63} +(-0.414558 + 1.07550i) q^{64} +(-6.96855 + 0.896645i) q^{65} +(-0.804938 + 0.640113i) q^{66} +(3.86849 - 3.32654i) q^{67} +(-4.60486 - 1.07985i) q^{68} +(-0.204773 + 0.475957i) q^{69} +(-7.61276 + 1.83668i) q^{70} +(-3.48116 + 2.84181i) q^{71} +(-16.7416 - 7.52240i) q^{72} +(-3.87349 - 2.76907i) q^{73} +(-0.255250 + 3.18464i) q^{74} +(0.0684865 - 0.609086i) q^{75} +(-1.28058 - 4.59257i) q^{76} +(-2.71568 + 5.09782i) q^{77} +(2.52811 + 0.308862i) q^{78} +(9.82431 - 1.45630i) q^{79} +(-7.99315 - 2.53508i) q^{80} +(-4.00209 + 7.75005i) q^{81} +(8.66894 - 19.7994i) q^{82} +(-2.89781 + 0.898693i) q^{83} +(1.95655 + 0.0250387i) q^{84} +(-0.221509 + 1.29386i) q^{85} +(-14.4325 + 4.57735i) q^{86} +(0.826521 - 0.403630i) q^{87} +(-12.2352 + 7.29200i) q^{88} +(-2.23128 - 1.46905i) q^{89} +(-3.28043 + 8.67553i) q^{90} +(13.7155 - 4.06192i) q^{91} +(-6.72522 + 11.2026i) q^{92} +(-0.123702 - 1.54337i) q^{93} +(-12.4004 - 0.396845i) q^{94} +(-1.25066 + 0.432179i) q^{95} +(0.734055 + 0.456804i) q^{96} +(2.47342 - 0.126717i) q^{97} +(-1.67466 + 0.701528i) q^{98} +(3.17767 + 6.05816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9}+O(q^{10}) $ 39690 * q - 489 * q^2 - 487 * q^3 - 565 * q^4 - 485 * q^5 - 477 * q^6 - 489 * q^7 - 485 * q^8 - 558 * q^9	\( 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9} - 471 q^{10} - 477 q^{11} - 463 q^{12} - 483 q^{13} - 473 q^{14} - 461 q^{15} - 543 q^{16} - 481 q^{17} - 457 q^{18} - 473 q^{19} - 449 q^{20} - 449 q^{21} - 459 q^{22} - 473 q^{23} - 405 q^{24} - 552 q^{25} - 437 q^{26} - 451 q^{27} - 455 q^{28} - 455 q^{29} - 379 q^{30} - 459 q^{31} - 437 q^{32} - 447 q^{33} - 423 q^{34} - 439 q^{35} - 459 q^{36} - 475 q^{37} - 423 q^{38} - 439 q^{39} - 413 q^{40} - 455 q^{41} - 407 q^{42} - 457 q^{43} - 413 q^{44} - 397 q^{45} - 415 q^{46} - 467 q^{47} - 393 q^{48} - 524 q^{49} - 429 q^{50} - 403 q^{51} - 391 q^{52} - 431 q^{53} - 379 q^{54} - 415 q^{55} - 371 q^{56} - 447 q^{57} - 431 q^{58} - 439 q^{59} - 261 q^{60} - 431 q^{61} - 383 q^{62} - 445 q^{63} - 447 q^{64} - 415 q^{65} - 345 q^{66} - 439 q^{67} - 409 q^{68} - 367 q^{69} - 345 q^{70} - 415 q^{71} - 341 q^{72} - 465 q^{73} - 359 q^{74} - 339 q^{75} - 361 q^{76} - 363 q^{77} - 341 q^{78} - 423 q^{79} - 249 q^{80} - 420 q^{81} - 371 q^{82} - 433 q^{83} - 215 q^{84} - 409 q^{85} - 369 q^{86} - 329 q^{87} - 255 q^{88} - 393 q^{89} - 251 q^{90} - 373 q^{91} - 387 q^{92} - 369 q^{93} - 317 q^{94} - 393 q^{95} - 149 q^{96} - 415 q^{97} - 307 q^{98} - 299 q^{99}+O(q^{100}) \) 39690 * q - 489 * q^2 - 487 * q^3 - 565 * q^4 - 485 * q^5 - 477 * q^6 - 489 * q^7 - 485 * q^8 - 558 * q^9 - 471 * q^10 - 477 * q^11 - 463 * q^12 - 483 * q^13 - 473 * q^14 - 461 * q^15 - 543 * q^16 - 481 * q^17 - 457 * q^18 - 473 * q^19 - 449 * q^20 - 449 * q^21 - 459 * q^22 - 473 * q^23 - 405 * q^24 - 552 * q^25 - 437 * q^26 - 451 * q^27 - 455 * q^28 - 455 * q^29 - 379 * q^30 - 459 * q^31 - 437 * q^32 - 447 * q^33 - 423 * q^34 - 439 * q^35 - 459 * q^36 - 475 * q^37 - 423 * q^38 - 439 * q^39 - 413 * q^40 - 455 * q^41 - 407 * q^42 - 457 * q^43 - 413 * q^44 - 397 * q^45 - 415 * q^46 - 467 * q^47 - 393 * q^48 - 524 * q^49 - 429 * q^50 - 403 * q^51 - 391 * q^52 - 431 * q^53 - 379 * q^54 - 415 * q^55 - 371 * q^56 - 447 * q^57 - 431 * q^58 - 439 * q^59 - 261 * q^60 - 431 * q^61 - 383 * q^62 - 445 * q^63 - 447 * q^64 - 415 * q^65 - 345 * q^66 - 439 * q^67 - 409 * q^68 - 367 * q^69 - 345 * q^70 - 415 * q^71 - 341 * q^72 - 465 * q^73 - 359 * q^74 - 339 * q^75 - 361 * q^76 - 363 * q^77 - 341 * q^78 - 423 * q^79 - 249 * q^80 - 420 * q^81 - 371 * q^82 - 433 * q^83 - 215 * q^84 - 409 * q^85 - 369 * q^86 - 329 * q^87 - 255 * q^88 - 393 * q^89 - 251 * q^90 - 373 * q^91 - 387 * q^92 - 369 * q^93 - 317 * q^94 - 393 * q^95 - 149 * q^96 - 415 * q^97 - 307 * q^98 - 299 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/983\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{337}{491}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.805572	+	2.40575i	−0.569626	+	1.70113i	0.134379	+	0.990930i	$0.457096\pi$
$2$	−0.805572	+	2.40575i	−0.569626	+	1.70113i	−0.704005	+	0.710195i	$0.748607\pi$
$3$	−0.153383	−	0.0861729i	−0.0885559	−	0.0497520i	0.444897	−	0.895582i	$-0.353240\pi$
$3$	−0.153383	−	0.0861729i	−0.0885559	−	0.0497520i	−0.533453	+	0.845830i	$0.679106\pi$
$4$	−3.54199	−	2.67165i	−1.77100	−	1.33582i
$5$	−0.680394	+	1.02626i	−0.304281	+	0.458956i	−0.953391	−	0.301739i	$-0.902433\pi$
$5$	−0.680394	+	1.02626i	−0.304281	+	0.458956i	0.649109	+	0.760695i	$0.275142\pi$
$6$	0.330872	−	0.299584i	0.135078	−	0.122305i
$7$	1.03475	−	2.28334i	0.391099	−	0.863020i	−0.606586	−	0.795018i	$-0.707462\pi$
$7$	1.03475	−	2.28334i	0.391099	−	0.863020i	0.997685	−	0.0680028i	$-0.0216627\pi$
$8$	5.09698	−	3.49786i	1.80205	−	1.23668i
$9$	−1.54443	−	2.53574i	−0.514811	−	0.845246i
$10$	−1.92082	−	2.46358i	−0.607416	−	0.779054i
$11$	−2.29938	−	0.147324i	−0.693290	−	0.0444198i	−0.286686	−	0.958024i	$-0.592554\pi$
$11$	−2.29938	−	0.147324i	−0.693290	−	0.0444198i	−0.406604	+	0.913605i	$0.633287\pi$
$12$	0.313059	+	0.715010i	0.0903722	+	0.206406i
$13$	3.73418	+	4.31455i	1.03568	+	1.19664i	0.980165	+	0.198182i	$0.0635036\pi$
$13$	3.73418	+	4.31455i	1.03568	+	1.19664i	0.0555107	+	0.998458i	$0.482321\pi$
$14$	4.65958	+	4.32875i	1.24533	+	1.15691i
$15$	0.192797	−	0.0987793i	0.0497799	−	0.0255047i
$16$	1.87110	+	6.54813i	0.467775	+	1.63703i
$17$	0.975206	−	0.430705i	0.236522	−	0.104461i	−0.282356	−	0.959310i	$-0.591116\pi$
$17$	0.975206	−	0.430705i	0.236522	−	0.104461i	0.518878	+	0.854849i	$0.326350\pi$
$18$	7.34452	−	1.67281i	1.73112	−	0.394284i
$19$	0.853792	+	0.652610i	0.195873	+	0.149719i	0.700585	−	0.713569i	$-0.252923\pi$
$19$	0.853792	+	0.652610i	0.195873	+	0.149719i	−0.504711	+	0.863288i	$0.668401\pi$
$20$	5.15175	−	1.81722i	1.15197	−	0.406343i
$21$	−0.355475	+	0.261058i	−0.0775711	+	0.0569676i
$22$	2.20674	−	5.41307i	0.470479	−	1.15407i
$23$	−0.310345	−	2.92870i	−0.0647114	−	0.610676i	−0.978751	−	0.205052i	$-0.934264\pi$
$23$	−0.310345	−	2.92870i	−0.0647114	−	0.610676i	0.914040	−	0.405625i	$-0.132946\pi$
$24$	−1.08321	+	0.0972912i	−0.221110	+	0.0198595i
$25$	1.35635	+	3.20899i	0.271270	+	0.641797i
$26$	−13.3879	+	5.50785i	−2.62558	+	1.08018i
$27$	0.0369481	+	1.04950i	0.00711067	+	0.201976i
$28$	−9.76535	+	5.32307i	−1.84548	+	1.00597i
$29$	−2.97208	+	4.30127i	−0.551901	+	0.798726i	−0.995222	−	0.0976372i	$-0.968872\pi$
$29$	−2.97208	+	4.30127i	−0.551901	+	0.798726i	0.443321	+	0.896363i	$0.353800\pi$
$30$	0.0823270	+	0.543395i	0.0150308	+	0.0992099i
$31$	4.90984	+	7.30375i	0.881833	+	1.31179i	0.949397	+	0.314077i	$0.101695\pi$
$31$	4.90984	+	7.30375i	0.881833	+	1.31179i	−0.0675642	+	0.997715i	$0.521523\pi$
$32$	−4.90937	−	0.220030i	−0.867862	−	0.0388962i
$33$	0.339992	+	0.220742i	0.0591849	+	0.0384262i
$34$	0.250572	+	2.69307i	0.0429727	+	0.461858i
$35$	1.63926	+	2.61549i	0.277085	+	0.442098i
$36$	−1.30423	+	13.1077i	−0.217372	+	2.18462i
$37$	1.22224	−	0.303170i	0.200935	−	0.0498409i	−0.138988	−	0.990294i	$-0.544385\pi$
$37$	1.22224	−	0.303170i	0.200935	−	0.0498409i	0.339923	+	0.940453i	$0.389599\pi$
$38$	−2.25781	+	1.52829i	−0.366265	+	0.247921i
$39$	−0.200964	−	0.983565i	−0.0321800	−	0.157496i
$40$	0.121751	+	7.61073i	0.0192505	+	1.20336i
$41$	−8.48523	−	0.762121i	−1.32517	−	0.119023i	−0.595795	−	0.803137i	$-0.703163\pi$
$41$	−8.48523	−	0.762121i	−1.32517	−	0.119023i	−0.729376	+	0.684113i	$0.760189\pi$
$42$	−0.341681	−	1.06549i	−0.0527226	−	0.164408i
$43$	3.51714	+	4.82143i	0.536358	+	0.735262i	0.987574	−	0.157153i	$-0.0502316\pi$
$43$	3.51714	+	4.82143i	0.536358	+	0.735262i	−0.451216	+	0.892415i	$0.649010\pi$
$44$	7.75080	+	6.66496i	1.16848	+	1.00478i
$45$	3.65314	+	0.140314i	0.544578	+	0.0209167i
$46$	7.29574	+	1.61267i	1.07570	+	0.237775i
$47$	1.40364	+	4.68444i	0.204742	+	0.683296i	0.997296	+	0.0734942i	$0.0234150\pi$
$47$	1.40364	+	4.68444i	0.204742	+	0.683296i	−0.792554	+	0.609802i	$0.791249\pi$
$48$	0.277276	−	1.16561i	0.0400214	−	0.168242i
$49$	0.471797	+	0.538126i	0.0673995	+	0.0768751i
$50$	−8.81267	+	0.677972i	−1.24630	+	0.0958797i
$51$	−0.186695	−	0.0179734i	−0.0261426	−	0.00251678i
$52$	−1.69949	−	25.2585i	−0.235677	−	3.50273i
$53$	1.18501	−	1.08683i	0.162774	−	0.149288i	−0.590396	−	0.807113i	$-0.701029\pi$
$53$	1.18501	−	1.08683i	0.162774	−	0.149288i	0.753171	+	0.657825i	$0.228523\pi$
$54$	−2.55460	−	0.756559i	−0.347637	−	0.102955i
$55$	1.71568	−	2.25952i	0.231342	−	0.304674i
$56$	−2.71269	−	15.2575i	−0.362498	−	2.03887i
$57$	−0.0747202	−	0.173673i	−0.00989693	−	0.0230036i
$58$	−7.95357	−	10.6151i	−1.04436	−	1.39383i
$59$	8.33995	+	0.641605i	1.08577	+	0.0835298i	0.607222	−	0.794532i	$-0.292284\pi$
$59$	8.33995	+	0.641605i	1.08577	+	0.0835298i	0.478547	+	0.878062i	$0.341164\pi$
$60$	−0.946788	−	0.165210i	−0.122230	−	0.0213285i
$61$	1.43961	+	1.22200i	0.184323	+	0.156461i	0.734550	−	0.678555i	$-0.237393\pi$
$61$	1.43961	+	1.22200i	0.184323	+	0.156461i	−0.550226	+	0.835016i	$0.685459\pi$
$62$	−21.5263	+	5.92817i	−2.73384	+	0.752878i
$63$	−7.38805	+	0.902607i	−0.930807	+	0.113718i
$64$	−0.414558	+	1.07550i	−0.0518198	+	0.134438i
$65$	−6.96855	+	0.896645i	−0.864342	+	0.111215i
$66$	−0.804938	+	0.640113i	−0.0990810	+	0.0787924i
$67$	3.86849	−	3.32654i	0.472611	−	0.406401i	−0.383220	−	0.923657i	$-0.625185\pi$
$67$	3.86849	−	3.32654i	0.472611	−	0.406401i	0.855831	+	0.517256i	$0.173046\pi$
$68$	−4.60486	−	1.07985i	−0.558422	−	0.130951i
$69$	−0.204773	+	0.475957i	−0.0246518	+	0.0572985i
$70$	−7.61276	+	1.83668i	−0.909899	+	0.219525i
$71$	−3.48116	+	2.84181i	−0.413138	+	0.337260i	−0.816053	−	0.577977i	$-0.803842\pi$
$71$	−3.48116	+	2.84181i	−0.413138	+	0.337260i	0.402915	+	0.915237i	$0.367997\pi$
$72$	−16.7416	−	7.52240i	−1.97302	−	0.886523i
$73$	−3.87349	−	2.76907i	−0.453357	−	0.324095i	0.331845	−	0.943334i	$-0.392329\pi$
$73$	−3.87349	−	2.76907i	−0.453357	−	0.324095i	−0.785202	+	0.619239i	$0.787441\pi$
$74$	−0.255250	+	3.18464i	−0.0296722	+	0.370206i
$75$	0.0684865	−	0.609086i	0.00790814	−	0.0703312i
$76$	−1.28058	−	4.59257i	−0.146893	−	0.526804i
$77$	−2.71568	+	5.09782i	−0.309480	+	0.580951i
$78$	2.52811	+	0.308862i	0.286252	+	0.0349717i
$79$	9.82431	−	1.45630i	1.10532	−	0.163846i	0.431049	−	0.902329i	$-0.358144\pi$
$79$	9.82431	−	1.45630i	1.10532	−	0.163846i	0.674273	+	0.738483i	$0.264457\pi$
$80$	−7.99315	−	2.53508i	−0.893662	−	0.283430i
$81$	−4.00209	+	7.75005i	−0.444677	+	0.861117i
$82$	8.66894	−	19.7994i	0.957325	−	2.18648i
$83$	−2.89781	+	0.898693i	−0.318076	+	0.0986444i	−0.451113	−	0.892467i	$-0.648973\pi$
$83$	−2.89781	+	0.898693i	−0.318076	+	0.0986444i	0.133037	+	0.991111i	$0.457527\pi$
$84$	1.95655	+	0.0250387i	0.213477	+	0.00273195i
$85$	−0.221509	+	1.29386i	−0.0240261	+	0.140339i
$86$	−14.4325	+	4.57735i	−1.55630	+	0.493589i
$87$	0.826521	−	0.403630i	0.0886123	−	0.0432737i
$88$	−12.2352	+	7.29200i	−1.30428	+	0.777330i
$89$	−2.23128	−	1.46905i	−0.236515	−	0.155719i	0.426108	−	0.904673i	$-0.359885\pi$
$89$	−2.23128	−	1.46905i	−0.236515	−	0.155719i	−0.662623	+	0.748954i	$0.730557\pi$
$90$	−3.28043	+	8.67553i	−0.345788	+	0.914481i
$91$	13.7155	−	4.06192i	1.43778	−	0.425805i
$92$	−6.72522	+	11.2026i	−0.701153	+	1.16795i
$93$	−0.123702	−	1.54337i	−0.0128273	−	0.160040i
$94$	−12.4004	−	0.396845i	−1.27900	−	0.0409314i
$95$	−1.25066	+	0.432179i	−0.128315	+	0.0443407i
$96$	0.734055	+	0.456804i	0.0749191	+	0.0466223i
$97$	2.47342	−	0.126717i	0.251137	−	0.0128662i	0.0748103	−	0.997198i	$-0.476165\pi$
$97$	2.47342	−	0.126717i	0.251137	−	0.0128662i	0.176327	+	0.984332i	$0.443578\pi$
$98$	−1.67466	+	0.701528i	−0.169167	+	0.0708650i
$99$	3.17767	+	6.05816i	0.319368	+	0.608868i
$100$	3.76911	−	14.9899i	0.376911	−	1.49899i
$101$	0.767512	+	0.556131i	0.0763703	+	0.0553371i	0.624282	−	0.781199i	$-0.285392\pi$
$101$	0.767512	+	0.556131i	0.0763703	+	0.0553371i	−0.547912	+	0.836536i	$0.684577\pi$
$102$	0.193636	−	0.434664i	0.0191728	−	0.0430382i
$103$	−0.358905	−	0.139662i	−0.0353640	−	0.0137613i	0.344898	−	0.938640i	$-0.387914\pi$
$103$	−0.358905	−	0.139662i	−0.0353640	−	0.0137613i	−0.380262	+	0.924879i	$0.624166\pi$
$104$	34.1247	+	8.92951i	3.34620	+	0.875610i
$105$	−0.0260500	−	0.542432i	−0.00254222	−	0.0529359i
$106$	1.66004	+	3.72637i	0.161237	+	0.361938i
$107$	0.797803	−	3.78112i	0.0771265	−	0.365534i	−0.922672	−	0.385585i	$-0.874000\pi$
$107$	0.797803	−	3.78112i	0.0771265	−	0.365534i	0.999799	+	0.0200504i	$0.00638266\pi$
$108$	2.67302	−	3.81603i	0.257212	−	0.367198i
$109$	8.45474	+	10.0252i	0.809817	+	0.960240i	0.999768	−	0.0215536i	$-0.00686126\pi$
$109$	8.45474	+	10.0252i	0.809817	+	0.960240i	−0.189950	+	0.981794i	$0.560833\pi$
$110$	4.05375	+	5.94770i	0.386510	+	0.567091i
$111$	−0.213596	−	0.0588228i	−0.0202737	−	0.00558321i
$112$	16.8877	+	2.50333i	1.59574	+	0.236542i
$113$	11.5929	+	5.66136i	1.09056	+	0.532576i	0.894069	−	0.447929i	$-0.147838\pi$
$113$	11.5929	+	5.66136i	1.09056	+	0.532576i	0.196495	+	0.980505i	$0.437044\pi$
$114$	0.478008	−	0.0398520i	0.0447695	−	0.00373248i
$115$	3.21676	+	1.67417i	0.299964	+	0.156118i
$116$	22.0186	−	7.29471i	2.04437	−	0.677297i
$117$	5.17336	−	16.1324i	0.478277	−	1.49144i
$118$	−8.26197	+	19.5470i	−0.760576	+	1.79945i
$119$	0.0256492	−	2.67240i	0.00235126	−	0.244978i
$120$	0.637165	−	1.17785i	0.0581649	−	0.107523i
$121$	−5.64460	−	0.726292i	−0.513146	−	0.0660266i
$122$	−4.09954	+	2.47894i	−0.371155	+	0.224433i
$123$	1.23582	+	0.848094i	0.111430	+	0.0764701i
$124$	2.12245	−	38.9872i	0.190602	−	3.50115i
$125$	−10.2670	−	1.92723i	−0.918308	−	0.172377i
$126$	3.78016	−	18.5009i	0.336763	−	1.64820i
$127$	6.62416	+	15.9560i	0.587799	+	1.41587i	0.887040	+	0.461692i	$0.152757\pi$
$127$	6.62416	+	15.9560i	0.587799	+	1.41587i	−0.299241	+	0.954178i	$0.596734\pi$
$128$	−9.82730	−	8.12773i	−0.868619	−	0.718397i
$129$	−0.123993	−	1.04261i	−0.0109170	−	0.0917967i
$130$	3.45656	−	17.4869i	0.303161	−	1.53370i
$131$	−11.7208	−	6.00516i	−1.02405	−	0.524673i	−0.139064	−	0.990283i	$-0.544409\pi$
$131$	−11.7208	−	6.00516i	−1.02405	−	0.524673i	−0.884990	+	0.465610i	$0.845835\pi$
$132$	−0.614503	−	1.69020i	−0.0534856	−	0.147113i
$133$	2.37359	−	1.27421i	0.205816	−	0.110488i
$134$	4.88649	+	11.9864i	0.422128	+	1.03547i
$135$	−1.10220	−	0.676154i	−0.0948619	−	0.0581941i
$136$	3.46406	−	5.60642i	0.297040	−	0.480747i
$137$	−7.27787	−	12.8577i	−0.621791	−	1.09851i	−0.985929	−	0.167165i	$-0.946539\pi$
$137$	−7.27787	−	12.8577i	−0.621791	−	1.09851i	0.364138	−	0.931345i	$-0.381364\pi$
$138$	−0.980076	−	0.876051i	−0.0834296	−	0.0745744i
$139$	4.88838	−	9.31960i	0.414627	−	0.790478i	−0.585164	−	0.810915i	$-0.698970\pi$
$139$	4.88838	−	9.31960i	0.414627	−	0.790478i	0.999791	+	0.0204367i	$0.00650564\pi$
$140$	1.18144	−	13.6436i	0.0998499	−	1.15309i
$141$	0.188377	−	0.839471i	0.0158642	−	0.0706962i
$142$	−4.03236	−	10.6641i	−0.338388	−	0.894912i
$143$	−7.95068	−	10.4709i	−0.664869	−	0.875623i
$144$	13.7146	−	14.8578i	1.14288	−	1.23815i
$145$	−2.39203	−	5.97668i	−0.198647	−	0.496336i
$146$	9.78206	−	7.08798i	0.809569	−	0.586605i
$147$	−0.0259939	−	0.123196i	−0.00214394	−	0.0101610i
$148$	−5.13913	−	2.19157i	−0.422434	−	0.180146i
$149$	4.75168	+	18.3990i	0.389272	+	1.50730i	0.802486	+	0.596671i	$0.203510\pi$
$149$	4.75168	+	18.3990i	0.389272	+	1.50730i	−0.413214	+	0.910634i	$0.635594\pi$
$150$	1.41014	+	0.655424i	0.115137	+	0.0535152i
$151$	0.557280	−	0.200593i	0.0453508	−	0.0163240i	−0.315904	−	0.948791i	$-0.602308\pi$
$151$	0.557280	−	0.200593i	0.0453508	−	0.0163240i	0.361255	+	0.932467i	$0.382348\pi$
$152$	6.63450	+	0.339896i	0.538129	+	0.0275692i
$153$	−2.59830	−	1.80767i	−0.210060	−	0.146142i
$154$	−10.0764	−	10.6399i	−0.811982	−	0.857389i
$155$	−10.8362	+	0.0693345i	−0.870381	+	0.00556908i
$156$	−1.91593	+	4.02068i	−0.153397	+	0.321912i
$157$	2.66983	+	2.89238i	0.213076	+	0.230837i	0.832228	−	0.554434i	$-0.187065\pi$
$157$	2.66983	+	2.89238i	0.213076	+	0.230837i	−0.619152	+	0.785271i	$0.712523\pi$
$158$	−4.41070	+	24.8080i	−0.350897	+	1.97362i
$159$	−0.275417	+	0.0645861i	−0.0218420	+	0.00512201i
$160$	3.56611	−	4.88857i	0.281926	−	0.386475i
$161$	−7.00834	−	2.32185i	−0.552335	−	0.182987i
$162$	−15.4208	−	15.8713i	−1.21157	−	1.24696i
$163$	0.226979	−	0.0578450i	0.0177784	−	0.00453077i	−0.238055	−	0.971252i	$-0.576510\pi$
$163$	0.226979	−	0.0578450i	0.0177784	−	0.00453077i	0.255833	+	0.966721i	$0.417650\pi$
$164$	28.0185	+	25.3690i	2.18788	+	1.98099i
$165$	−0.457866	+	0.198728i	−0.0356448	+	0.0154709i
$166$	0.172361	−	7.69538i	0.0133778	−	0.597277i
$167$	1.76133	+	9.55159i	0.136296	+	0.739124i	0.979487	+	0.201510i	$0.0645847\pi$
$167$	1.76133	+	9.55159i	0.136296	+	0.739124i	−0.843191	+	0.537614i	$0.819326\pi$
$168$	−0.898705	+	2.57401i	−0.0693366	+	0.198589i
$169$	−2.80612	+	19.3571i	−0.215855	+	1.48901i
$170$	−2.93427	−	1.57520i	−0.225048	−	0.120812i
$171$	0.336223	−	3.17291i	0.0257116	−	0.242638i
$172$	0.423512	−	26.4740i	0.0322925	−	2.01863i
$173$	11.8997	−	2.23371i	0.904717	−	0.169826i	0.288572	−	0.957458i	$-0.406820\pi$
$173$	11.8997	−	2.23371i	0.904717	−	0.169826i	0.616146	+	0.787632i	$0.288693\pi$
$174$	0.305213	+	2.31356i	0.0231382	+	0.175390i
$175$	8.73068	+	0.223497i	0.659978	+	0.0168948i
$176$	−3.33768	−	15.3323i	−0.251587	−	1.15572i
$177$	−1.22392	−	0.817089i	−0.0919955	−	0.0614162i
$178$	5.33163	−	4.18448i	0.399622	−	0.313640i
$179$	10.4816	+	5.03589i	0.783434	+	0.376400i	0.781745	−	0.623598i	$-0.214330\pi$
$179$	10.4816	+	5.03589i	0.783434	+	0.376400i	0.00168922	+	0.999999i	$0.499462\pi$
$180$	−12.5645	−	10.2569i	−0.936505	−	0.764505i
$181$	−4.55947	−	9.11363i	−0.338903	−	0.677411i	0.658251	−	0.752798i	$-0.271296\pi$
$181$	−4.55947	−	9.11363i	−0.338903	−	0.677411i	−0.997154	+	0.0753874i	$0.975981\pi$
$182$	−1.27684	+	36.2683i	−0.0946460	+	2.68839i
$183$	−0.115509	−	0.311490i	−0.00853869	−	0.0230260i
$184$	−11.8260	−	13.8420i	−0.871824	−	1.02044i
$185$	−0.520474	+	1.46061i	−0.0382660	+	0.107386i
$186$	3.81262	+	0.945699i	0.279555	+	0.0693420i
$187$	−2.30582	+	0.846685i	−0.168619	+	0.0619157i
$188$	7.54351	−	20.3423i	0.550167	−	1.48361i
$189$	2.43459	+	1.00160i	0.177091	+	0.0728560i
$190$	−0.0322193	−	3.35693i	−0.00233743	−	0.243538i
$191$	10.6260	+	5.61702i	0.768868	+	0.406433i	0.805273	−	0.592904i	$-0.202019\pi$
$191$	10.6260	+	5.61702i	0.768868	+	0.406433i	−0.0364057	+	0.999337i	$0.511591\pi$
$192$	0.156266	−	0.129240i	0.0112775	−	0.00932712i
$193$	18.6651	+	17.7902i	1.34354	+	1.28057i	0.928776	+	0.370641i	$0.120862\pi$
$193$	18.6651	+	17.7902i	1.34354	+	1.28057i	0.414767	+	0.909928i	$0.363863\pi$
$194$	−1.68767	+	6.05251i	−0.121167	+	0.434545i
$195$	1.14613	+	0.462970i	0.0820758	+	0.0331540i
$196$	−0.233417	−	3.16651i	−0.0166726	−	0.226179i
$197$	8.31466	−	2.23266i	0.592395	−	0.159070i	0.0493609	−	0.998781i	$-0.484282\pi$
$197$	8.31466	−	2.23266i	0.592395	−	0.159070i	0.543034	+	0.839711i	$0.317275\pi$
$198$	−17.1343	+	2.76440i	−1.21768	+	0.196457i
$199$	−11.7831	+	18.2764i	−0.835283	+	1.29558i	0.117851	+	0.993031i	$0.462399\pi$
$199$	−11.7831	+	18.2764i	−0.835283	+	1.29558i	−0.953134	+	0.302548i	$0.902163\pi$
$200$	18.1379	+	11.6118i	1.28254	+	0.821080i
$201$	−0.880019	+	0.176877i	−0.0620718	+	0.0124759i
$202$	−1.95620	+	1.39844i	−0.137638	+	0.0983940i
$203$	6.74589	+	11.2370i	0.473469	+	0.788683i
$204$	0.613255	+	0.562446i	0.0429364	+	0.0393791i
$205$	6.55543	−	8.18949i	0.457851	−	0.571979i
$206$	0.625117	−	0.750929i	0.0435540	−	0.0523197i
$207$	−6.94711	+	5.31014i	−0.482858	+	0.369080i
$208$	−21.2652	+	32.5249i	−1.47448	+	2.25519i
$209$	−1.86705	−	1.62638i	−0.129147	−	0.112499i
$210$	1.32594	+	0.374298i	0.0914987	+	0.0258290i
$211$	−1.79919	−	10.9293i	−0.123862	−	0.752402i	−0.974119	−	0.226035i	$-0.927424\pi$
$211$	−1.79919	−	10.9293i	−0.123862	−	0.752402i	0.850258	−	0.526367i	$-0.176446\pi$
$212$	−7.10095	+	0.683616i	−0.487695	+	0.0469509i
$213$	0.778839	−	0.135904i	0.0533652	−	0.00931196i
$214$	8.45375	+	4.96528i	0.577886	+	0.339420i
$215$	−7.34107	+	0.329015i	−0.500657	+	0.0224387i
$216$	3.85932	+	5.22003i	0.262594	+	0.355178i
$217$	21.7574	−	3.65326i	1.47699	−	0.248000i
$218$	−30.9291	+	12.2640i	−2.09478	+	0.830623i
$219$	0.355510	+	0.758518i	0.0240231	+	0.0512559i
$220$	−12.1136	+	3.41952i	−0.816696	+	0.230544i
$221$	5.49989	+	2.59924i	0.369963	+	0.174844i
$222$	0.313580	−	0.466474i	0.0210461	−	0.0313077i
$223$	−8.46165	+	11.4450i	−0.566634	+	0.766417i	−0.990231	−	0.139434i	$-0.955472\pi$
$223$	−8.46165	+	11.4450i	−0.566634	+	0.766417i	0.423598	+	0.905850i	$0.360767\pi$
$224$	−5.58237	+	10.9821i	−0.372988	+	0.733770i
$225$	6.04236	−	8.39541i	0.402824	−	0.559694i
$226$	−22.9587	+	23.3289i	−1.52719	+	1.55182i
$227$	3.48436	+	5.88916i	0.231265	+	0.390877i	0.953793	−	0.300465i	$-0.0971419\pi$
$227$	3.48436	+	5.88916i	0.231265	+	0.390877i	−0.722527	+	0.691342i	$0.757020\pi$
$228$	−0.199336	+	0.814776i	−0.0132013	+	0.0539598i
$229$	4.45738	−	20.4759i	0.294552	−	1.35309i	−0.557739	−	0.830017i	$-0.688331\pi$
$229$	4.45738	−	20.4759i	0.294552	−	1.35309i	0.852290	−	0.523069i	$-0.175213\pi$
$230$	−6.61898	+	6.39006i	−0.436443	+	0.421348i
$231$	0.855834	−	0.547903i	0.0563097	−	0.0360494i
$232$	−0.103396	+	32.3194i	−0.00678827	+	2.12187i
$233$	−9.86859	+	6.05399i	−0.646513	+	0.396610i	−0.807103	−	0.590411i	$-0.798966\pi$
$233$	−9.86859	+	6.05399i	−0.646513	+	0.396610i	0.160590	+	0.987021i	$0.448660\pi$
$234$	34.6432	+	25.4417i	2.26469	+	1.66317i
$235$	−5.76247	−	1.74677i	−0.375902	−	0.113947i
$236$	−27.8259	−	24.5540i	−1.81131	−	1.59833i
$237$	−1.63238	−	0.623219i	−0.106034	−	0.0404824i
$238$	6.40846	+	2.21451i	0.415399	+	0.143546i
$239$	17.5379	+	21.6244i	1.13443	+	1.39877i	0.904983	+	0.425448i	$0.139883\pi$
$239$	17.5379	+	21.6244i	1.13443	+	1.39877i	0.229448	+	0.973321i	$0.426308\pi$
$240$	1.00756	+	1.07763i	0.0650378	+	0.0695608i
$241$	−12.4175	−	0.0794526i	−0.799881	−	0.00511799i	−0.394076	−	0.919078i	$-0.628935\pi$
$241$	−12.4175	−	0.0794526i	−0.799881	−	0.00511799i	−0.405805	+	0.913960i	$0.633009\pi$
$242$	6.29441	−	12.9944i	0.404620	−	0.835314i
$243$	3.91304	−	2.57630i	0.251022	−	0.165270i
$244$	−1.83434	−	8.17444i	−0.117432	−	0.523315i
$245$	−0.873263	+	0.118048i	−0.0557907	+	0.00754179i
$246$	−3.03585	+	2.28988i	−0.193559	+	0.145997i
$247$	0.372501	+	6.12069i	0.0237017	+	0.389450i
$248$	50.5728	+	20.0531i	3.21138	+	1.27338i
$249$	0.521919	+	0.111868i	0.0330753	+	0.00708937i
$250$	12.9073	−	23.1473i	0.816327	−	1.46397i
$251$	6.68298	−	22.3035i	0.421826	−	1.40778i	−0.438819	−	0.898575i	$-0.644603\pi$
$251$	6.68298	−	22.3035i	0.421826	−	1.40778i	0.860645	−	0.509206i	$-0.170061\pi$
$252$	28.5799	+	16.5413i	1.80036	+	1.04200i
$253$	0.282135	+	6.77992i	0.0177377	+	0.426250i
$254$	−43.7225	+	3.08237i	−2.74340	+	0.193405i
$255$	0.145472	−	0.179369i	0.00910979	−	0.0112325i
$256$	25.5127	−	15.8766i	1.59454	−	0.992288i
$257$	−20.5271	+	14.2810i	−1.28044	+	0.890822i	−0.997661	−	0.0683618i	$-0.978223\pi$
$257$	−20.5271	+	14.2810i	−1.28044	+	0.890822i	−0.282782	+	0.959184i	$0.591257\pi$
$258$	2.60815	+	0.541601i	0.162376	+	0.0337186i
$259$	0.572474	−	3.10449i	0.0355718	−	0.192904i
$260$	27.0781	+	15.4416i	1.67931	+	0.957648i
$261$	15.4971	+	0.893390i	0.959245	+	0.0552995i
$262$	23.8889	−	23.3598i	1.47586	−	1.44318i
$263$	−6.47330	−	26.4593i	−0.399161	−	1.63155i	−0.726874	−	0.686771i	$-0.759027\pi$
$263$	−6.47330	−	26.4593i	−0.399161	−	1.63155i	0.327713	−	0.944777i	$-0.393722\pi$
$264$	2.50505	−	0.0641269i	0.154175	−	0.00394674i
$265$	0.309096	+	1.95560i	0.0189876	+	0.120132i
$266$	1.15333	+	6.73674i	0.0707153	+	0.413056i
$267$	0.215648	+	0.417604i	0.0131975	+	0.0255569i
$268$	−22.5895	+	1.44733i	−1.37987	+	0.0884099i
$269$	15.0691	+	16.9673i	0.918777	+	1.03452i	0.999287	+	0.0377637i	$0.0120234\pi$
$269$	15.0691	+	16.9673i	0.918777	+	1.03452i	−0.0805097	+	0.996754i	$0.525655\pi$
$270$	2.51456	−	2.10692i	0.153031	−	0.128223i
$271$	−10.5931	+	0.203360i	−0.643485	+	0.0123533i	−0.339915	−	0.940456i	$-0.610398\pi$
$271$	−10.5931	+	0.203360i	−0.643485	+	0.0123533i	−0.303570	+	0.952809i	$0.598179\pi$
$272$	4.64502	+	5.57988i	0.281646	+	0.338330i
$273$	−2.45376	−	0.558875i	−0.148508	−	0.0338246i
$274$	36.7954	−	7.15094i	2.22289	−	0.432004i
$275$	−2.64601	−	7.57851i	−0.159560	−	0.457001i
$276$	1.99689	−	1.13875i	0.120199	−	0.0685450i
$277$	−5.44549	+	2.70258i	−0.327188	+	0.162383i	−0.600676	−	0.799493i	$-0.705102\pi$
$277$	−5.44549	+	2.70258i	−0.327188	+	0.162383i	0.273488	+	0.961875i	$0.411823\pi$
$278$	18.4827	+	19.2678i	1.10852	+	1.15561i
$279$	10.9375	−	23.7302i	0.654810	−	1.42069i
$280$	17.5039	+	7.59721i	1.04606	+	0.454020i
$281$	2.06056	+	4.54694i	0.122923	+	0.271248i	0.962144	−	0.272542i	$-0.0878645\pi$
$281$	2.06056	+	4.54694i	0.122923	+	0.271248i	−0.839221	+	0.543790i	$0.816989\pi$
$282$	1.86781	+	1.12944i	0.111226	+	0.0672574i
$283$	18.7171	+	14.8845i	1.11262	+	0.884791i	0.994133	−	0.108165i	$-0.0344975\pi$
$283$	18.7171	+	14.8845i	1.11262	+	0.884791i	0.118486	+	0.992956i	$0.462196\pi$
$284$	19.9226	−	0.765206i	1.18219	−	0.0454066i
$285$	0.229073	+	0.0414841i	0.0135691	+	0.00245730i
$286$	31.5953	−	10.6923i	1.86827	−	0.632249i
$287$	−10.5203	+	18.5860i	−0.620992	+	1.09710i
$288$	7.02425	+	12.7887i	0.413908	+	0.753581i
$289$	−10.6849	+	11.7253i	−0.628526	+	0.689721i
$290$	16.3054	−	0.939987i	0.957484	−	0.0551979i
$291$	−0.390301	−	0.193705i	−0.0228798	−	0.0113552i
$292$	6.32189	+	20.1566i	0.369961	+	1.17958i
$293$	−7.15901	+	1.87332i	−0.418234	+	0.109440i	−0.456281	−	0.889836i	$-0.650819\pi$
$293$	−7.15901	+	1.87332i	−0.418234	+	0.109440i	0.0380475	+	0.999276i	$0.487886\pi$
$294$	0.317318	+	0.0367081i	0.0185064	+	0.00214086i
$295$	−6.33290	+	8.12239i	−0.368716	+	0.472904i
$296$	5.16929	−	5.82047i	0.300459	−	0.338308i
$297$	0.0696583	−	2.41864i	0.00404198	−	0.140344i
$298$	−48.0913	−	3.39036i	−2.78585	−	0.196398i
$299$	11.4771	−	12.2753i	0.663739	−	0.709899i
$300$	−1.86984	+	1.97440i	−0.107955	+	0.113992i
$301$	14.6483	−	3.04183i	0.844315	−	0.175328i
$302$	0.0336479	+	1.50227i	0.00193622	+	0.0864460i
$303$	−0.0698001	−	0.151440i	−0.00400991	−	0.00870000i
$304$	−2.67585	+	6.81184i	−0.153470	+	0.390686i
$305$	−2.23359	+	0.645973i	−0.127895	+	0.0369883i
$306$	6.44193	−	4.79465i	0.368260	−	0.274092i
$307$	−8.36341	+	8.28353i	−0.477325	+	0.472766i	−0.901478	−	0.432825i	$-0.857517\pi$
$307$	−8.36341	+	8.28353i	−0.477325	+	0.472766i	0.424153	+	0.905591i	$0.360572\pi$
$308$	23.2385	−	10.8011i	1.32414	−	0.615450i
$309$	0.0430149	+	0.0523498i	0.00244703	+	0.00297807i
$310$	8.56250	−	26.1250i	0.486317	−	1.48380i
$311$	4.51643	−	3.01517i	0.256103	−	0.170975i	−0.420566	−	0.907262i	$-0.638168\pi$
$311$	4.51643	−	3.01517i	0.256103	−	0.170975i	0.676669	+	0.736288i	$0.263423\pi$
$312$	−4.46468	−	4.31026i	−0.252763	−	0.244021i
$313$	−30.0982	−	6.04950i	−1.70125	−	0.341938i	−0.752654	−	0.658417i	$-0.771227\pi$
$313$	−30.0982	−	6.04950i	−1.70125	−	0.341938i	−0.948600	+	0.316479i	$0.897499\pi$
$314$	−9.10910	+	4.09294i	−0.514056	+	0.230978i
$315$	4.10047	−	8.19617i	0.231036	−	0.461802i
$316$	−38.6883	−	21.0889i	−2.17639	−	1.18635i
$317$	8.34040	−	4.20605i	0.468444	−	0.236235i	−0.200291	−	0.979737i	$-0.564189\pi$
$317$	8.34040	−	4.20605i	0.468444	−	0.236235i	0.668734	+	0.743501i	$0.266836\pi$
$318$	0.0664901	−	0.714614i	0.00372858	−	0.0400736i
$319$	7.46763	−	9.45241i	0.418107	−	0.529233i
$320$	−0.821680	−	1.15721i	−0.0459333	−	0.0646899i
$321$	−0.448200	+	0.511211i	−0.0250161	+	0.0285330i
$322$	11.2315	−	14.9899i	0.625908	−	0.835356i
$323$	1.11371	+	0.268696i	0.0619682	+	0.0149507i
$324$	34.8808	−	16.7584i	1.93782	−	0.931025i
$325$	−8.78046	+	17.8350i	−0.487053	+	0.989306i
$326$	−0.0436870	+	0.592654i	−0.00241960	+	0.0328240i
$327$	−0.432915	−	2.26627i	−0.0239403	−	0.125325i
$328$	−45.9148	+	25.7956i	−2.53522	+	1.42432i
$329$	12.1486	+	1.64225i	0.669773	+	0.0905399i
$330$	−0.109246	−	1.26160i	−0.00601381	−	0.0694489i
$331$	−15.6851	−	6.57060i	−0.862132	−	0.361153i	−0.0894847	−	0.995988i	$-0.528522\pi$
$331$	−15.6851	−	6.57060i	−0.862132	−	0.361153i	−0.772647	+	0.634836i	$0.781068\pi$
$332$	12.6650	+	4.55877i	0.695083	+	0.250195i
$333$	−2.65643	−	2.63106i	−0.145571	−	0.144181i
$334$	−24.3976	−	3.45717i	−1.33498	−	0.189168i
$335$	0.781792	+	6.23342i	0.0427139	+	0.340568i
$336$	−2.37457	−	1.83923i	−0.129544	−	0.100338i
$337$	15.6309	−	24.9397i	0.851471	−	1.35855i	−0.0807767	−	0.996732i	$-0.525740\pi$
$337$	15.6309	−	24.9397i	0.851471	−	1.35855i	0.932248	−	0.361820i	$-0.117844\pi$
$338$	−44.3079	−	22.3444i	−2.41003	−	1.21537i
$339$	−1.29030	−	1.86735i	−0.0700792	−	0.101420i
$340$	4.24133	−	3.99105i	0.230018	−	0.216445i
$341$	−10.2136	−	17.5175i	−0.553096	−	0.948623i
$342$	7.36238	+	3.36488i	0.398112	+	0.181952i
$343$	18.5103	−	5.61101i	0.999464	−	0.302966i
$344$	34.7915	+	12.2723i	1.87583	+	0.661678i
$345$	−0.349128	−	0.533988i	−0.0187964	−	0.0287489i
$346$	−4.21231	+	30.4272i	−0.226455	+	1.63577i
$347$	2.12320	+	0.937723i	0.113979	+	0.0503396i	0.460212	−	0.887809i	$-0.347773\pi$
$347$	2.12320	+	0.937723i	0.113979	+	0.0503396i	−0.346233	+	0.938149i	$0.612539\pi$
$348$	−4.00589	−	0.778518i	−0.214738	−	0.0417329i
$349$	−3.17983	−	21.9350i	−0.170212	−	1.17415i	−0.881823	−	0.471580i	$-0.843684\pi$
$349$	−3.17983	−	21.9350i	−0.170212	−	1.17415i	0.711611	−	0.702574i	$-0.247966\pi$
$350$	−7.57087	+	20.8238i	−0.404680	+	1.11308i
$351$	−4.39014	+	4.07844i	−0.234328	+	0.217691i
$352$	11.2561	+	1.22920i	0.599952	+	0.0655166i
$353$	−9.52924	−	9.55978i	−0.507190	−	0.508816i	0.407371	−	0.913263i	$-0.366446\pi$
$353$	−9.52924	−	9.55978i	−0.507190	−	0.508816i	−0.914561	+	0.404447i	$0.867464\pi$
$354$	2.95167	−	2.28623i	0.156880	−	0.121512i
$355$	−0.547864	−	5.50612i	−0.0290776	−	0.292234i
$356$	3.97838	+	11.1646i	0.210854	+	0.591720i
$357$	−0.234222	+	0.407691i	−0.0123964	+	0.0215773i
$358$	−20.5588	+	21.1595i	−1.08657	+	1.11831i
$359$	−1.86856	+	0.972498i	−0.0986187	+	0.0513265i	−0.510265	−	0.860017i	$-0.670453\pi$
$359$	−1.86856	+	0.972498i	−0.0986187	+	0.0513265i	0.411647	+	0.911344i	$0.364954\pi$
$360$	19.1108	−	12.0630i	1.00723	−	0.635776i
$361$	−4.68296	−	17.2197i	−0.246472	−	0.906301i
$362$	25.5981	−	3.62728i	1.34541	−	0.190646i
$363$	0.803201	+	0.597813i	0.0421571	+	0.0313770i
$364$	−59.4323	−	22.2557i	−3.11510	−	1.16652i
$365$	5.47727	−	2.09114i	0.286693	−	0.109455i
$366$	0.842418	−	0.0269597i	0.0440339	−	0.00140920i
$367$	1.66628	+	14.8191i	0.0869789	+	0.773548i	0.958869	+	0.283847i	$0.0916109\pi$
$367$	1.66628	+	14.8191i	0.0869789	+	0.773548i	−0.871891	+	0.489701i	$0.837106\pi$
$368$	18.5968	−	7.51207i	0.969426	−	0.391594i
$369$	11.1723	+	22.6934i	0.581609	+	1.18137i
$370$	−3.09459	−	2.42876i	−0.160880	−	0.126265i
$371$	−1.25542	−	3.83039i	−0.0651779	−	0.198864i
$372$	−3.68519	+	5.79709i	−0.191068	+	0.300565i
$373$	0.774196	−	18.6045i	0.0400863	−	0.963306i	−0.855332	−	0.518080i	$-0.826647\pi$
$373$	0.774196	−	18.6045i	0.0400863	−	0.963306i	0.895418	−	0.445226i	$-0.146877\pi$
$374$	−0.179408	−	6.22931i	−0.00927695	−	0.322110i
$375$	1.40871	+	1.18034i	0.0727455	+	0.0609527i
$376$	23.5398	+	18.9668i	1.21397	+	0.978137i
$377$	−29.6563	+	3.23856i	−1.52738	+	0.166794i
$378$	−4.37085	+	5.05017i	−0.224812	+	0.259753i
$379$	6.05376	+	1.87744i	0.310961	+	0.0964378i	0.447740	−	0.894164i	$-0.352229\pi$
$379$	6.05376	+	1.87744i	0.310961	+	0.0964378i	−0.136779	+	0.990602i	$0.543675\pi$
$380$	5.58446	+	1.81055i	0.286477	+	0.0928794i
$381$	0.358943	−	3.01821i	0.0183892	−	0.154628i
$382$	−22.0732	+	21.0385i	−1.12936	+	1.07643i
$383$	−7.49232	−	14.0645i	−0.382839	−	0.718660i	0.614700	−	0.788761i	$-0.289277\pi$
$383$	−7.49232	−	14.0645i	−0.382839	−	0.718660i	−0.997540	+	0.0701007i	$0.977668\pi$
$384$	0.806953	+	2.09351i	0.0411797	+	0.106834i
$385$	−3.38395	−	6.25551i	−0.172462	−	0.318810i
$386$	−57.8350	+	30.5723i	−2.94372	+	1.55609i
$387$	6.79391	−	16.3649i	0.345354	−	0.831876i
$388$	−9.09937	−	6.15927i	−0.461950	−	0.312690i
$389$	−18.0805	−	6.63904i	−0.916716	−	0.336613i	−0.157551	−	0.987511i	$-0.550360\pi$
$389$	−18.0805	−	6.63904i	−0.916716	−	0.336613i	−0.759165	+	0.650898i	$0.774392\pi$
$390$	−2.03708	+	2.38434i	−0.103152	+	0.120736i
$391$	−1.56406	−	2.72242i	−0.0790977	−	0.137679i
$392$	4.28702	+	1.09254i	0.216527	+	0.0551815i
$393$	1.28030	+	1.93111i	0.0645825	+	0.0974116i
$394$	−1.32683	+	21.8016i	−0.0668448	+	1.09835i
$395$	−5.18987	+	11.0731i	−0.261130	+	0.557150i
$396$	4.93001	−	29.9476i	0.247743	−	1.50492i
$397$	0.386319	−	5.74162i	0.0193888	−	0.288164i	−0.977592	−	0.210510i	$-0.932487\pi$
$397$	0.386319	−	5.74162i	0.0193888	−	0.288164i	0.996980	−	0.0776534i	$-0.0247428\pi$
$398$	−34.4764	−	43.0702i	−1.72814	−	2.15892i
$399$	−0.473872	−	0.00909711i	−0.0237233	−	0.000455425i
$400$	−18.4750	+	14.8859i	−0.923750	+	0.744294i
$401$	21.3023	−	21.3705i	1.06378	−	1.06719i	0.0661950	−	0.997807i	$-0.478914\pi$
$401$	21.3023	−	21.3705i	1.06378	−	1.06719i	0.997590	−	0.0693868i	$-0.0221043\pi$
$402$	0.283397	−	2.25960i	0.0141346	−	0.112698i
$403$	−13.1781	+	48.4573i	−0.656449	+	2.41383i
$404$	−1.23273	−	4.02034i	−0.0613309	−	0.200019i
$405$	−5.23056	−	9.38026i	−0.259908	−	0.466109i
$406$	−32.4678	+	7.17674i	−1.61135	+	0.356176i
$407$	−2.85506	+	0.517039i	−0.141520	+	0.0256287i
$408$	−1.01445	+	0.561424i	−0.0502228	+	0.0277946i
$409$	−18.4765	−	20.5379i	−0.913605	−	1.01553i	−0.999815	−	0.0192548i	$-0.993871\pi$
$409$	−18.4765	−	20.5379i	−0.913605	−	1.01553i	0.0862097	−	0.996277i	$-0.472524\pi$
$410$	14.4210	+	22.3680i	0.712204	+	1.10468i
$411$	0.00831571	+	2.59932i	0.000410184	+	0.128215i
$412$	0.898110	+	1.45355i	0.0442467	+	0.0716113i
$413$	10.0948	−	18.3790i	0.496731	−	0.904372i
$414$	−7.17848	−	20.9907i	−0.352803	−	1.03164i
$415$	1.04936	−	3.58536i	0.0515111	−	0.175999i
$416$	−17.3832	−	22.0033i	−0.852279	−	1.07880i
$417$	−1.55289	+	1.00823i	−0.0760455	+	0.0493730i
$418$	5.41672	−	3.18149i	0.264941	−	0.155612i
$419$	29.4680	−	25.0136i	1.43961	−	1.22199i	0.506576	−	0.862195i	$-0.330911\pi$
$419$	29.4680	−	25.0136i	1.43961	−	1.22199i	0.933030	−	0.359798i	$-0.117154\pi$
$420$	−1.35692	+	1.99089i	−0.0662108	+	0.0971452i
$421$	−10.9227	+	1.12212i	−0.532342	+	0.0546890i	−0.364640	−	0.931149i	$-0.618808\pi$
$421$	−10.9227	+	1.12212i	−0.532342	+	0.0546890i	−0.167702	+	0.985838i	$0.553635\pi$
$422$	27.7425	+	4.47590i	1.35049	+	0.217884i
$423$	9.71070	−	10.7941i	0.472150	−	0.524826i
$424$	2.23840	−	9.68458i	0.108706	−	0.470325i
$425$	2.70485	+	2.54524i	0.131204	+	0.123462i
$426$	−0.300461	+	1.98318i	−0.0145574	+	0.0960852i
$427$	4.27987	−	2.02266i	0.207117	−	0.0978832i
$428$	−12.9276	+	11.2612i	−0.624880	+	0.544332i
$429$	0.317191	+	2.29120i	0.0153141	+	0.110620i
$430$	5.12223	−	17.9259i	0.247016	−	0.864462i
$431$	−2.13369	−	10.7945i	−0.102776	−	0.519951i	−0.997332	−	0.0729948i	$-0.976744\pi$
$431$	−2.13369	−	10.7945i	−0.102776	−	0.519951i	0.894556	−	0.446956i	$-0.147492\pi$
$432$	−6.80312	+	2.20566i	−0.327315	+	0.106120i
$433$	−22.2082	+	0.284207i	−1.06726	+	0.0136581i	−0.544450	−	0.838793i	$-0.683262\pi$
$433$	−22.2082	+	0.284207i	−1.06726	+	0.0136581i	−0.522807	+	0.852451i	$0.675115\pi$
$434$	−8.73829	+	55.2859i	−0.419452	+	2.65381i
$435$	−0.148131	+	1.12285i	−0.00710232	+	0.0538366i
$436$	−3.16280	−	58.0973i	−0.151471	−	2.78235i
$437$	1.64633	−	2.70304i	0.0787546	−	0.129304i
$438$	−2.11120	+	0.244228i	−0.100877	+	0.0116697i
$439$	14.7453	−	5.73792i	0.703757	−	0.273856i	0.0160777	−	0.999871i	$-0.494882\pi$
$439$	14.7453	−	5.73792i	0.703757	−	0.273856i	0.687679	+	0.726015i	$0.258630\pi$
$440$	0.841290	−	17.5179i	0.0401069	−	0.835134i
$441$	0.635887	−	2.02745i	0.0302804	−	0.0965453i
$442$	−10.6837	+	11.1375i	−0.508171	+	0.529758i
$443$	7.73972	+	19.7028i	0.367725	+	0.936110i	0.988377	+	0.152023i	$0.0485789\pi$
$443$	7.73972	+	19.7028i	0.367725	+	0.936110i	−0.620652	+	0.784086i	$0.713132\pi$
$444$	0.599403	+	0.779004i	0.0284464	+	0.0369699i
$445$	3.02577	−	1.29033i	0.143435	−	0.0611677i
$446$	−20.7175	−	29.5765i	−0.981002	−	1.40049i
$447$	0.856668	−	3.23157i	0.0405190	−	0.152848i
$448$	2.02677	+	2.05945i	0.0957559	+	0.0973000i
$449$	24.4884	−	3.79030i	1.15568	−	0.178875i	0.453756	−	0.891126i	$-0.350084\pi$
$449$	24.4884	−	3.79030i	1.15568	−	0.178875i	0.701925	+	0.712251i	$0.252324\pi$
$450$	15.3297	+	21.2995i	0.722651	+	1.00407i
$451$	19.3985	+	3.00248i	0.913441	+	0.141381i
$452$	−25.9366	−	51.0245i	−1.21996	−	2.39999i
$453$	−0.102763	−	0.0172549i	−0.00482824	−	0.000810705i
$454$	−16.9748	+	3.63838i	−0.796666	+	0.170758i
$455$	−5.16336	+	16.8394i	−0.242062	+	0.789441i
$456$	−0.988332	−	0.623849i	−0.0462829	−	0.0292144i
$457$	−18.5792	−	1.54897i	−0.869098	−	0.0724575i	−0.359781	−	0.933037i	$-0.617149\pi$
$457$	−18.5792	−	1.54897i	−0.869098	−	0.0724575i	−0.509317	+	0.860579i	$0.670102\pi$
$458$	45.6692	+	27.2182i	2.13398	+	1.27182i
$459$	0.488056	+	1.00756i	0.0227805	+	0.0470290i
$460$	−6.92092	−	14.5240i	−0.322690	−	0.677183i
$461$	−7.71575	+	19.2784i	−0.359358	+	0.897885i	0.632961	+	0.774183i	$0.281839\pi$
$461$	−7.71575	+	19.2784i	−0.359358	+	0.897885i	−0.992319	+	0.123702i	$0.960523\pi$
$462$	0.628684	+	2.50030i	0.0292490	+	0.116325i
$463$	16.8573	−	15.0681i	0.783424	−	0.700272i	−0.175329	−	0.984510i	$-0.556099\pi$
$463$	16.8573	−	15.0681i	0.783424	−	0.700272i	0.958754	+	0.284238i	$0.0917406\pi$
$464$	−33.7263	−	11.4135i	−1.56571	−	0.529857i
$465$	1.66806	+	0.923148i	0.0773544	+	0.0428100i
$466$	−6.61456	−	28.6183i	−0.306414	−	1.32572i
$467$	6.93191	−	11.8890i	0.320771	−	0.550158i	−0.658534	−	0.752551i	$-0.728823\pi$
$467$	6.93191	−	11.8890i	0.320771	−	0.550158i	0.979304	+	0.202393i	$0.0648719\pi$
$468$	−61.4242	+	43.3196i	−2.83934	+	2.00245i
$469$	−3.59269	−	12.2752i	−0.165895	−	0.566816i
$470$	8.84439	−	12.4559i	0.407961	−	0.574550i
$471$	−0.160263	−	0.673711i	−0.00738451	−	0.0310429i
$472$	44.7528	−	25.9017i	2.05991	−	1.19222i
$473$	−7.37693	−	11.6045i	−0.339192	−	0.533575i
$474$	2.81431	−	3.42505i	0.129266	−	0.157318i
$475$	−0.936177	+	3.62498i	−0.0429547	+	0.166325i
$476$	−7.23055	+	9.39708i	−0.331412	+	0.430714i
$477$	−4.58610	−	1.32634i	−0.209983	−	0.0607290i
$478$	−66.1511	+	24.7718i	−3.02568	+	1.13303i
$479$	−11.2203	+	9.90093i	−0.512667	+	0.452385i	−0.878117	−	0.478446i	$-0.841200\pi$
$479$	−11.2203	+	9.90093i	−0.512667	+	0.452385i	0.365450	+	0.930831i	$0.380915\pi$
$480$	−0.968244	+	0.442523i	−0.0441941	+	0.0201983i
$481$	5.87211	+	4.14132i	0.267745	+	0.188828i
$482$	10.1943	−	29.8094i	0.464339	−	1.35778i
$483$	0.874882	+	0.960062i	0.0398085	+	0.0436844i
$484$	18.0527	+	17.6529i	0.820579	+	0.802405i
$485$	−1.55285	+	2.62458i	−0.0705114	+	0.119176i
$486$	3.04572	+	11.4892i	0.138157	+	0.521161i
$487$	−4.14614	+	4.91628i	−0.187880	+	0.222778i	−0.850224	−	0.526422i	$-0.823533\pi$
$487$	−4.14614	+	4.91628i	−0.187880	+	0.222778i	0.662344	+	0.749200i	$0.269562\pi$
$488$	11.6120	+	1.19294i	0.525652	+	0.0540018i
$489$	−0.0397994	−	0.0106870i	−0.00179979	−	0.000483282i
$490$	0.419483	−	2.19595i	0.0189503	−	0.0992030i
$491$	11.4843	+	34.2966i	0.518279	+	1.54778i	0.807109	+	0.590403i	$0.201031\pi$
$491$	11.4843	+	34.2966i	0.518279	+	1.54778i	−0.288830	+	0.957380i	$0.593266\pi$
$492$	−2.11145	−	6.30562i	−0.0951915	−	0.284279i
$493$	−1.04581	+	5.47471i	−0.0471009	+	0.246569i
$494$	−15.0250	−	4.03451i	−0.676005	−	0.181521i
$495$	−8.37930	−	0.860830i	−0.376622	−	0.0386914i
$496$	−38.6391	+	45.8163i	−1.73495	+	2.05721i
$497$	2.88667	+	10.8892i	0.129485	+	0.488449i
$498$	−0.689571	+	1.16549i	−0.0309004	+	0.0522269i
$499$	−13.8162	−	13.5103i	−0.618500	−	0.604802i	0.321113	−	0.947041i	$-0.395943\pi$
$499$	−13.8162	−	13.5103i	−0.618500	−	0.604802i	−0.939613	+	0.342239i	$0.888815\pi$
$500$	31.2167	+	34.2561i	1.39605	+	1.53198i
$501$	0.552930	−	1.61683i	0.0247031	−	0.0722348i
$502$	48.2730	+	34.0446i	2.15453	+	1.51949i
$503$	10.4844	−	4.79176i	0.467477	−	0.213654i	−0.167980	−	0.985790i	$-0.553724\pi$
$503$	10.4844	−	4.79176i	0.467477	−	0.213654i	0.635457	+	0.772137i	$0.280812\pi$
$504$	−34.4995	+	30.4429i	−1.53673	+	1.35604i
$505$	−1.09294	+	0.409277i	−0.0486354	+	0.0182126i
$506$	−16.5381	−	4.78297i	−0.735209	−	0.212629i
$507$	2.09847	−	2.72724i	0.0931963	−	0.121121i
$508$	19.1662	−	74.2136i	0.850363	−	3.29270i
$509$	20.7992	−	25.3129i	0.921908	−	1.12197i	−0.0703182	−	0.997525i	$-0.522401\pi$
$509$	20.7992	−	25.3129i	0.921908	−	1.12197i	0.992226	−	0.124450i	$-0.0397167\pi$
$510$	0.314329	+	0.494463i	0.0139187	+	0.0218952i
$511$	−10.3308	+	5.97919i	−0.457008	+	0.264504i
$512$	11.7403	+	49.3537i	0.518852	+	2.18114i
$513$	−0.653368	+	0.920167i	−0.0288469	+	0.0406264i
$514$	−17.8205	−	60.8874i	−0.786027	−	2.68563i
$515$	0.387526	−	0.273304i	0.0170764	−	0.0120432i
$516$	−2.34631	+	4.02418i	−0.103290	+	0.177155i
$517$	−2.53738	−	10.9781i	−0.111594	−	0.482817i
$518$	7.00748	+	3.87812i	0.307891	+	0.170395i
$519$	−2.01770	−	0.682818i	−0.0885672	−	0.0299724i
$520$	−32.3822	+	28.9452i	−1.42005	+	1.26933i
$521$	−6.48720	−	25.7998i	−0.284209	−	1.13031i	−0.930226	−	0.366988i	$-0.880389\pi$
$521$	−6.48720	−	25.7998i	−0.284209	−	1.13031i	0.646016	−	0.763324i	$-0.276434\pi$
$522$	−14.6333	+	36.5625i	−0.640482	+	1.60030i
$523$	−3.75009	−	7.86978i	−0.163980	−	0.344122i	0.804207	−	0.594349i	$-0.202590\pi$
$523$	−3.75009	−	7.86978i	−0.163980	−	0.344122i	−0.968187	+	0.250228i	$0.919495\pi$
$524$	25.4714	+	52.5842i	1.11272	+	2.29715i
$525$	−1.31988	−	0.786629i	−0.0576044	−	0.0343313i
$526$	68.8692	+	5.74169i	3.00284	+	0.250350i
$527$	7.93387	+	5.00797i	0.345605	+	0.218150i
$528$	−0.809287	+	2.63934i	−0.0352197	+	0.114862i
$529$	14.0082	−	3.00253i	0.609054	−	0.130545i
$530$	−4.95370	−	0.831771i	−0.215175	−	0.0361298i
$531$	−11.2536	−	22.1388i	−0.488363	−	0.960744i
$532$	−11.8115	−	1.82817i	−0.512092	−	0.0792612i
$533$	−28.3972	−	39.4558i	−1.23002	−	1.70902i
$534$	−1.17837	+	0.182387i	−0.0509931	+	0.00789267i
$535$	3.33758	+	3.39140i	0.144296	+	0.146623i
$536$	8.08184	−	30.4867i	0.349082	−	1.31683i
$537$	−1.17375	−	1.67565i	−0.0506511	−	0.0723099i
$538$	−52.9585	+	22.5840i	−2.28320	+	0.973667i
$539$	−1.00556	−	1.30686i	−0.0433126	−	0.0562906i
$540$	2.09752	+	5.33961i	0.0902629	+	0.229780i
$541$	−5.76528	+	6.01018i	−0.247869	+	0.258398i	−0.833932	−	0.551868i	$-0.813915\pi$
$541$	−5.76528	+	6.01018i	−0.247869	+	0.258398i	0.586063	+	0.810265i	$0.300677\pi$
$542$	8.04427	−	25.6482i	0.345531	−	1.10169i
$543$	−0.0860015	+	1.79078i	−0.00369068	+	0.0768498i
$544$	−4.88241	+	1.89992i	−0.209332	+	0.0814582i
$545$	−16.0410	+	1.85566i	−0.687120	+	0.0794877i
$546$	3.32119	−	5.45293i	0.142134	−	0.233364i
$547$	−0.623106	−	11.4458i	−0.0266421	−	0.489387i	−0.981397	−	0.191992i	$-0.938505\pi$
$547$	−0.623106	−	11.4458i	−0.0266421	−	0.489387i	0.954754	−	0.297395i	$-0.0961180\pi$
$548$	−8.57318	+	64.9859i	−0.366228	+	2.77606i
$549$	0.875281	−	5.53777i	0.0373561	−	0.236346i
$550$	20.3636	−	0.260601i	0.868306	−	0.0111121i
$551$	−5.34459	+	1.73278i	−0.227687	+	0.0738190i
$552$	0.621106	+	3.14221i	0.0264360	+	0.133741i
$553$	6.84050	−	23.9391i	0.290887	−	1.01800i
$554$	−2.11502	−	15.2776i	−0.0898586	−	0.649084i
$555$	0.205697	−	0.179182i	0.00873135	−	0.00760586i
$556$	−42.2133	+	19.9499i	−1.79024	+	0.846065i
$557$	1.23769	−	8.16929i	0.0524425	−	0.346144i	−0.947230	−	0.320554i	$-0.896131\pi$
$557$	1.23769	−	8.16929i	0.0524425	−	0.346144i	0.999673	−	0.0255893i	$-0.00814622\pi$
$558$	48.2782	+	45.4293i	2.04378	+	1.92318i
$559$	−7.66866	+	33.1790i	−0.324350	+	1.40332i
$560$	−14.0594	+	15.6279i	−0.594116	+	0.660399i
$561$	0.426636	+	0.0688323i	0.0180126	+	0.00290610i
$562$	−12.5987	+	1.29431i	−0.531446	+	0.0545970i
$563$	−15.7770	+	23.1481i	−0.664920	+	0.975578i	0.334529	+	0.942385i	$0.391423\pi$
$563$	−15.7770	+	23.1481i	−0.664920	+	0.975578i	−0.999449	+	0.0331924i	$0.989433\pi$
$564$	−2.91000	+	2.47012i	−0.122533	+	0.104011i
$565$	−13.6977	+	8.04531i	−0.576267	+	0.338469i
$566$	−50.8864	+	33.0383i	−2.13892	+	1.38870i
$567$	13.5548	+	17.1575i	0.569249	+	0.720547i
$568$	−7.80319	+	26.6612i	−0.327414	+	1.11868i
$569$	−10.2358	−	29.9307i	−0.429108	−	1.25476i	−0.922852	−	0.385155i	$-0.874148\pi$
$569$	−10.2358	−	29.9307i	−0.429108	−	1.25476i	0.493744	−	0.869607i	$-0.335628\pi$
$570$	−0.284335	+	0.517674i	−0.0119095	+	0.0216830i
$571$	−8.11811	−	13.1388i	−0.339732	−	0.549842i	0.635199	−	0.772349i	$-0.280918\pi$
$571$	−8.11811	−	13.1388i	−0.339732	−	0.549842i	−0.974931	+	0.222507i	$0.928576\pi$
$572$	0.186607	+	58.3294i	0.00780241	+	2.43887i
$573$	−1.14581	−	1.77723i	−0.0478669	−	0.0742448i
$574$	−36.2386	−	40.2816i	−1.51257	−	1.68132i
$575$	8.97722	−	4.96823i	0.374376	−	0.207190i
$576$	3.36745	−	0.609830i	0.140310	−	0.0254096i
$577$	−44.9124	+	9.92754i	−1.86973	+	0.413289i	−0.997167	−	0.0752141i	$-0.976036\pi$
$577$	−44.9124	+	9.92754i	−1.86973	+	0.413289i	−0.872562	+	0.488503i	$0.837543\pi$
$578$	−19.6006	−	35.1509i	−0.815277	−	1.46208i
$579$	−1.32988	−	4.33715i	−0.0552679	−	0.180246i
$580$	−7.49504	+	27.5600i	−0.311215	+	1.14437i
$581$	−0.946490	+	7.54660i	−0.0392670	+	0.313086i
$582$	0.780423	−	0.782923i	0.0323496	−	0.0324532i
$583$	−2.88492	+	2.32447i	−0.119481	+	0.0962696i
$584$	−29.4289	−	0.564959i	−1.21778	−	0.0233782i
$585$	13.0361	+	16.2856i	0.538977	+	0.673327i
$586$	1.26036	−	18.7319i	0.0520649	−	0.773808i
$587$	−2.59166	+	15.7431i	−0.106969	+	0.649788i	0.878212	+	0.478271i	$0.158736\pi$
$587$	−2.59166	+	15.7431i	−0.106969	+	0.649788i	−0.985181	+	0.171517i	$0.945133\pi$
$588$	−0.237065	+	0.505804i	−0.00977641	+	0.0208590i
$589$	−0.574518	+	9.44010i	−0.0236726	+	0.388972i
$590$	−14.4389	−	21.7786i	−0.594439	−	0.896610i
$591$	−1.46773	−	0.374046i	−0.0603741	−	0.0153862i
$592$	4.27213	+	7.43613i	0.175583	+	0.305623i
$593$	−16.7347	+	19.5875i	−0.687212	+	0.804361i	−0.988827	−	0.149069i	$-0.952372\pi$
$593$	−16.7347	+	19.5875i	−0.687212	+	0.804361i	0.301615	+	0.953430i	$0.402474\pi$
$594$	5.76254	+	2.11597i	0.236440	+	0.0868194i
$595$	2.72511	+	1.84460i	0.111719	+	0.0756214i
$596$	32.3253	−	77.8639i	1.32409	−	3.18943i
$597$	3.38226	−	1.78791i	0.138427	−	0.0731742i
$598$	20.2857	+	37.4998i	0.829544	+	1.53348i
$599$	0.329474	+	0.854765i	0.0134619	+	0.0349248i	0.939650	−	0.342136i	$-0.111151\pi$
$599$	0.329474	+	0.854765i	0.0134619	+	0.0349248i	−0.926188	+	0.377061i	$0.876935\pi$
$600$	−1.78142	−	3.34405i	−0.0727262	−	0.136520i
$601$	28.2890	−	26.9630i	1.15393	−	1.09984i	0.160310	−	0.987067i	$-0.448750\pi$
$601$	28.2890	−	26.9630i	1.15393	−	1.09984i	0.993620	−	0.112777i	$-0.0359746\pi$
$602$	−4.48238	+	37.6907i	−0.182688	+	1.53616i
$603$	−14.4099	−	4.67185i	−0.586815	−	0.190253i
$604$	−2.50980	−	0.778359i	−0.102122	−	0.0316710i
$605$	4.58591	−	5.29865i	0.186444	−	0.215421i
$606$	0.420557	−	0.0459261i	0.0170839	−	0.00186562i
$607$	−8.91348	−	7.18187i	−0.361787	−	0.291503i	0.429355	−	0.903136i	$-0.358741\pi$
$607$	−8.91348	−	7.18187i	−0.361787	−	0.291503i	−0.791142	+	0.611633i	$0.790513\pi$
$608$	−4.04799	−	3.39176i	−0.164168	−	0.137554i
$609$	−0.0663819	−	2.30488i	−0.00268993	−	0.0933985i
$610$	0.245262	−	5.89384i	0.00993037	−	0.238634i
$611$	−14.9698	+	23.5486i	−0.605613	+	0.952676i
$612$	4.37368	+	13.3445i	0.176795	+	0.539419i
$613$	11.4455	+	8.98293i	0.462281	+	0.362817i	0.821284	−	0.570519i	$-0.193258\pi$
$613$	11.4455	+	8.98293i	0.462281	+	0.362817i	−0.359003	+	0.933336i	$0.616883\pi$
$614$	−13.1908	−	26.7933i	−0.532337	−	1.08129i
$615$	−1.71121	+	0.691231i	−0.0690025	+	0.0278731i
$616$	3.98971	+	35.4825i	0.160750	+	1.42963i
$617$	−6.00713	+	0.192244i	−0.241838	+	0.00773947i	−0.152670	−	0.988277i	$-0.548787\pi$
$617$	−6.00713	+	0.192244i	−0.241838	+	0.00773947i	−0.0891677	+	0.996017i	$0.528421\pi$
$618$	−0.160592	+	0.0613118i	−0.00645997	+	0.00246632i
$619$	28.0832	+	10.5164i	1.12876	+	0.422688i	0.844231	−	0.535980i	$-0.180058\pi$
$619$	28.0832	+	10.5164i	1.12876	+	0.422688i	0.284527	+	0.958668i	$0.408164\pi$
$620$	38.5668	+	28.7048i	1.54888	+	1.15281i
$621$	3.06220	−	0.433917i	0.122882	−	0.0174125i
$622$	3.61545	+	13.2944i	0.144966	+	0.533055i
$623$	−5.66315	+	3.57466i	−0.226889	+	0.143216i
$624$	6.06449	−	3.15629i	0.242774	−	0.126353i
$625$	−3.17527	+	3.26804i	−0.127011	+	0.130722i
$626$	38.7999	−	67.5357i	1.55076	−	2.69927i
$627$	0.146224	+	0.410349i	0.00583963	+	0.0163878i
$628$	−1.72909	−	17.3777i	−0.0689983	−	0.693444i
$629$	1.06136	−	0.822078i	0.0423191	−	0.0327784i
$630$	16.4147	+	16.4673i	0.653979	+	0.656075i
$631$	−28.4806	−	3.11017i	−1.13380	−	0.123814i	−0.477722	−	0.878511i	$-0.658537\pi$
$631$	−28.4806	−	3.11017i	−1.13380	−	0.123814i	−0.656073	+	0.754697i	$0.727784\pi$
$632$	44.9804	−	41.7867i	1.78922	−	1.66219i
$633$	−0.665842	+	1.83141i	−0.0264648	+	0.0727920i
$634$	3.39992	+	23.4532i	0.135028	+	0.931447i
$635$	−20.8820	−	4.05829i	−0.828678	−	0.161048i
$636$	1.14808	+	0.507054i	0.0455242	+	0.0201060i
$637$	−0.559992	+	4.04505i	−0.0221877	+	0.160271i
$638$	16.7245	+	25.5799i	0.662128	+	1.01272i
$639$	12.5825	+	4.43834i	0.497756	+	0.175578i
$640$	15.0276	−	4.55529i	0.594017	−	0.180063i
$641$	−30.2014	−	13.8031i	−1.19288	−	0.545191i	−0.282625	−	0.959230i	$-0.591205\pi$
$641$	−30.2014	−	13.8031i	−1.19288	−	0.545191i	−0.910259	+	0.414039i	$0.864118\pi$
$642$	−0.868791	−	1.49008i	−0.0342885	−	0.0588086i
$643$	27.7589	−	26.1208i	1.09470	−	1.03011i	0.0953033	−	0.995448i	$-0.469618\pi$
$643$	27.7589	−	26.1208i	1.09470	−	1.03011i	0.999399	−	0.0346568i	$-0.0110338\pi$
$644$	18.6203	+	26.9478i	0.733743	+	1.06189i
$645$	1.15435	+	0.582136i	0.0454525	+	0.0229216i
$646$	−1.54359	+	2.46285i	−0.0607316	+	0.0968995i
$647$	−11.3517	−	8.79249i	−0.446281	−	0.345668i	0.364313	−	0.931277i	$-0.381304\pi$
$647$	−11.3517	−	8.79249i	−0.446281	−	0.345668i	−0.810594	+	0.585608i	$0.800856\pi$
$648$	6.71001	+	53.5006i	0.263594	+	2.10170i
$649$	−19.0822	−	2.70397i	−0.749042	−	0.106140i
$650$	−35.8333	−	35.4910i	−1.40550	−	1.39207i
$651$	−3.65203	−	1.31455i	−0.143134	−	0.0515212i
$652$	−0.958499	−	0.401521i	−0.0375377	−	0.0157248i
$653$	−0.785192	−	9.06758i	−0.0307269	−	0.354842i	−0.995710	−	0.0925296i	$-0.970505\pi$
$653$	−0.785192	−	9.06758i	−0.0307269	−	0.354842i	0.964983	−	0.262312i	$-0.0844851\pi$
$654$	5.80083	+	0.784156i	0.226830	+	0.0306629i
$655$	14.1376	−	7.94272i	0.552403	−	0.310348i
$656$	−10.8862	−	56.9884i	−0.425036	−	2.22502i
$657$	−1.03928	+	14.0988i	−0.0405462	+	0.550046i
$658$	−13.7374	+	27.9036i	−0.535540	+	1.08779i
$659$	1.41026	−	0.677560i	0.0549360	−	0.0263940i	−0.405391	−	0.914143i	$-0.632865\pi$
$659$	1.41026	−	0.677560i	0.0549360	−	0.0263940i	0.460327	+	0.887749i	$0.347732\pi$
$660$	2.15269	+	0.519365i	0.0837933	+	0.0202162i
$661$	−5.39805	+	7.20440i	−0.209960	+	0.280219i	−0.892899	−	0.450256i	$-0.851333\pi$
$661$	−5.39805	+	7.20440i	−0.209960	+	0.280219i	0.682939	+	0.730475i	$0.260701\pi$
$662$	28.4427	−	32.4414i	1.10546	−	1.26087i
$663$	−0.619608	−	0.872622i	−0.0240636	−	0.0338898i
$664$	−11.6266	+	14.7167i	−0.451199	+	0.571120i
$665$	−0.307311	+	3.30288i	−0.0119170	+	0.128080i
$666$	8.46962	−	4.27121i	0.328191	−	0.165506i
$667$	13.5195	+	7.36945i	0.523477	+	0.285346i
$668$	19.2799	−	38.5373i	0.745961	−	1.49105i
$669$	2.28413	−	1.02631i	0.0883095	−	0.0396796i
$670$	−15.6259	−	3.14067i	−0.603680	−	0.121335i
$671$	−3.13019	−	3.02193i	−0.120840	−	0.116660i
$672$	1.80260	−	1.20342i	0.0695368	−	0.0464228i
$673$	10.4561	−	31.9027i	0.403055	−	1.22976i	−0.522988	−	0.852340i	$-0.675183\pi$
$673$	10.4561	−	31.9027i	0.403055	−	1.22976i	0.926043	−	0.377417i	$-0.123188\pi$
$674$	47.4069	+	57.6949i	1.82605	+	2.22233i
$675$	−3.31771	+	1.54205i	−0.127699	+	0.0593536i
$676$	61.6546	−	61.0657i	2.37133	−	2.34868i
$677$	29.6324	−	22.0551i	1.13887	−	0.847645i	0.148887	−	0.988854i	$-0.452431\pi$
$677$	29.6324	−	22.0551i	1.13887	−	0.847645i	0.989980	+	0.141209i	$0.0450990\pi$
$678$	5.53181	−	1.59985i	0.212448	−	0.0614418i
$679$	2.27003	−	5.77877i	0.0871158	−	0.221769i
$680$	3.39671	+	7.36959i	0.130258	+	0.282611i
$681$	−0.0269572	−	1.20356i	−0.00103300	−	0.0461204i
$682$	50.3705	−	10.4598i	1.92878	−	0.400526i
$683$	−20.7597	+	21.9206i	−0.794348	+	0.838768i	−0.989877	−	0.141930i	$-0.954669\pi$
$683$	−20.7597	+	21.9206i	−0.794348	+	0.838768i	0.195529	+	0.980698i	$0.437358\pi$
$684$	−9.66779	+	10.3401i	−0.369657	+	0.395365i
$685$	18.1472	+	1.27935i	0.693367	+	0.0488813i
$686$	−1.41271	+	49.0514i	−0.0539374	+	1.87279i
$687$	−2.44816	+	2.75656i	−0.0934030	+	0.105169i
$688$	−24.9905	+	32.0520i	−0.952753	+	1.22197i
$689$	9.11425	+	1.05436i	0.347225	+	0.0401678i
$690$	1.56589	−	0.409751i	0.0596125	−	0.0155990i
$691$	8.98371	+	28.6435i	0.341756	+	1.08965i	0.954209	+	0.299142i	$0.0967005\pi$
$691$	8.98371	+	28.6435i	0.341756	+	1.08965i	−0.612452	+	0.790508i	$0.709817\pi$
$692$	−48.1163	−	23.8800i	−1.82911	−	0.907783i
$693$	17.1209	−	0.987003i	0.650370	−	0.0374932i
$694$	−3.96632	+	4.35249i	−0.150559	+	0.165218i
$695$	6.23829	+	11.3577i	0.236632	+	0.430823i
$696$	2.80092	−	4.94835i	0.106168	−	0.187567i
$697$	−8.60310	+	2.91141i	−0.325866	+	0.110277i
$698$	55.3318	+	10.0203i	2.09434	+	0.379276i
$699$	2.03537	−	0.0781764i	0.0769846	−	0.00295690i
$700$	−30.3269	−	24.1169i	−1.14625	−	0.911535i
$701$	2.40487	+	1.45420i	0.0908308	+	0.0549244i	0.562129	−	0.827049i	$-0.309982\pi$
$701$	2.40487	+	1.45420i	0.0908308	+	0.0549244i	−0.471298	+	0.881974i	$0.656215\pi$
$702$	−6.27514	−	13.8471i	−0.236840	−	0.522624i
$703$	1.24139	+	0.538802i	0.0468200	+	0.0203213i
$704$	1.11168	−	2.41192i	0.0418978	−	0.0909025i
$705$	0.733343	+	0.764495i	0.0276193	+	0.0287925i
$706$	30.6750	−	15.2239i	1.15447	−	0.572960i
$707$	2.06402	−	1.17703i	0.0776254	−	0.0442669i
$708$	2.15214	+	6.16401i	0.0808823	+	0.231658i
$709$	−45.9930	+	8.93843i	−1.72730	+	0.335690i	−0.954331	−	0.298751i	$-0.903430\pi$
$709$	−45.9930	+	8.93843i	−1.72730	+	0.335690i	−0.772972	+	0.634441i	$0.781230\pi$
$710$	13.6877	+	3.11755i	0.513691	+	0.117000i
$711$	−18.8658	−	22.6627i	−0.707522	−	0.849919i
$712$	−16.5113	+	0.316974i	−0.618787	+	0.0118791i
$713$	19.8668	−	16.6461i	0.744016	−	0.623402i
$714$	−0.792120	−	0.891906i	−0.0296444	−	0.0333787i
$715$	16.1555	−	1.03510i	0.604180	−	0.0387104i
$716$	−23.6717	−	45.8403i	−0.884654	−	1.71313i
$717$	−0.826575	−	4.82812i	−0.0308690	−	0.180309i
$718$	−0.834334	−	5.27871i	−0.0311371	−	0.197000i
$719$	4.83332	−	0.123728i	0.180252	−	0.00461429i	0.0646398	−	0.997909i	$-0.479410\pi$
$719$	4.83332	−	0.123728i	0.180252	−	0.00461429i	0.115613	+	0.993294i	$0.463117\pi$
$720$	5.91660	+	24.1838i	0.220499	+	0.901277i
$721$	−0.690273	+	0.674986i	−0.0257071	+	0.0251378i
$722$	45.1989	+	2.60567i	1.68213	+	0.0969729i
$723$	1.89779	+	1.08224i	0.0705795	+	0.0402489i
$724$	−8.19881	+	44.4617i	−0.304706	+	1.65241i
$725$	−17.8339	−	3.70334i	−0.662334	−	0.137539i
$726$	−2.08523	+	1.45072i	−0.0773901	+	0.0538414i
$727$	−23.1018	+	14.3763i	−0.856799	+	0.533188i	−0.884560	−	0.466427i	$-0.845541\pi$
$727$	−23.1018	+	14.3763i	−0.856799	+	0.533188i	0.0277610	+	0.999615i	$0.491162\pi$
$728$	55.6996	−	68.6784i	2.06437	−	2.54539i
$729$	25.2802	−	1.78221i	0.936303	−	0.0660078i
$730$	0.618437	+	14.8615i	0.0228894	+	0.550050i
$731$	5.50655	+	3.18704i	0.203667	+	0.117877i
$732$	−0.423058	+	1.41189i	−0.0156367	+	0.0521851i
$733$	3.84760	−	6.90012i	0.142114	−	0.254862i	−0.792990	−	0.609235i	$-0.791477\pi$
$733$	3.84760	−	6.90012i	0.142114	−	0.254862i	0.935104	+	0.354373i	$0.115306\pi$
$734$	−36.9933	−	7.92916i	−1.36545	−	0.292671i
$735$	0.144116	+	0.0571451i	0.00531582	+	0.00210783i
$736$	0.879196	+	14.4464i	0.0324076	+	0.532500i
$737$	−9.38521	+	7.07907i	−0.345709	+	0.260761i
$738$	−63.5948	+	8.59674i	−2.34096	+	0.316451i
$739$	1.82752	+	8.14402i	0.0672264	+	0.299583i	0.997782	−	0.0665681i	$-0.0212050\pi$
$739$	1.82752	+	8.14402i	0.0672264	+	0.299583i	−0.930556	+	0.366151i	$0.880675\pi$
$740$	5.74575	−	3.78294i	0.211218	−	0.139064i
$741$	0.470303	−	0.970912i	0.0172770	−	0.0356673i
$742$	10.2263	+	0.0654324i	0.375419	+	0.00240210i
$743$	33.0278	+	35.3247i	1.21167	+	1.29594i	0.943034	+	0.332696i	$0.107958\pi$
$743$	33.0278	+	35.3247i	1.21167	+	1.29594i	0.268638	+	0.963241i	$0.413426\pi$
$744$	−6.02899	−	7.43383i	−0.221033	−	0.272537i
$745$	−22.1151	−	7.64212i	−0.810235	−	0.279985i
$746$	44.1342	+	16.8498i	1.61587	+	0.616915i
$747$	6.75433	+	5.96012i	0.247128	+	0.218069i
$748$	10.4293	+	3.16140i	0.381331	+	0.115592i
$749$	−7.80804	−	5.73416i	−0.285300	−	0.209522i
$750$	−3.97443	+	2.43816i	−0.145126	+	0.0890290i
$751$	−0.102524	+	32.0468i	−0.00374115	+	1.16940i	0.809371	+	0.587298i	$0.199808\pi$
$751$	−0.102524	+	32.0468i	−0.00374115	+	1.16940i	−0.813112	+	0.582107i	$0.802228\pi$
$752$	−28.0480	+	17.9563i	−1.02281	+	0.654798i
$753$	−2.94701	+	2.84509i	−0.107395	+	0.103681i
$754$	16.0991	−	73.9547i	0.586295	−	2.69327i
$755$	−0.173310	+	0.708395i	−0.00630739	+	0.0257811i
$756$	−5.94737	−	10.0520i	−0.216304	−	0.365590i
$757$	−25.1172	+	25.5222i	−0.912901	+	0.927622i	−0.997632	−	0.0687820i	$-0.978089\pi$
$757$	−25.1172	+	25.5222i	−0.912901	+	0.927622i	0.0847305	+	0.996404i	$0.472997\pi$
$758$	−9.39341	+	13.0515i	−0.341184	+	0.474050i
$759$	0.540971	−	1.06424i	0.0196360	−	0.0386294i
$760$	−4.86289	+	6.57744i	−0.176396	+	0.238589i
$761$	−11.6039	+	17.2617i	−0.420641	+	0.625735i	−0.978999	−	0.203865i	$-0.934649\pi$
$761$	−11.6039	+	17.2617i	−0.420641	+	0.625735i	0.558358	+	0.829600i	$0.311432\pi$
$762$	6.97192	+	3.29492i	0.252566	+	0.119362i
$763$	31.6395	−	8.93145i	1.14543	−	0.323340i
$764$	−22.6304	−	48.2843i	−0.818738	−	1.74686i
$765$	3.62300	−	1.43659i	0.130990	−	0.0519401i
$766$	39.8712	−	6.69474i	1.44061	−	0.241891i
$767$	28.3747	+	38.3790i	1.02455	+	1.38578i
$768$	−5.28136	+	0.236702i	−0.190575	+	0.00854126i
$769$	20.0023	+	11.7483i	0.721300	+	0.423653i	0.820674	−	0.571397i	$-0.193598\pi$
$769$	20.0023	+	11.7483i	0.721300	+	0.423653i	−0.0993737	+	0.995050i	$0.531684\pi$
$770$	17.7752	−	3.10169i	0.640575	−	0.111777i
$771$	4.37914	−	0.421585i	0.157711	−	0.0151830i
$772$	−18.5824	−	112.879i	−0.668794	−	4.06262i
$773$	23.2090	+	6.55162i	0.834769	+	0.235645i	0.662176	−	0.749348i	$-0.269633\pi$
$773$	23.2090	+	6.55162i	0.834769	+	0.235645i	0.172592	+	0.984993i	$0.444786\pi$
$774$	33.8970	+	29.5276i	1.21840	+	1.06135i
$775$	−16.7782	+	25.6620i	−0.602690	+	0.921808i
$776$	12.1637	−	9.29753i	0.436652	−	0.333762i
$777$	−0.355331	+	0.426846i	−0.0127474	+	0.0153130i
$778$	30.5370	−	38.1489i	1.09481	−	1.36771i
$779$	−6.74726	−	6.18824i	−0.241746	−	0.221717i
$780$	−2.82267	−	4.70188i	−0.101068	−	0.168354i
$781$	8.42319	−	6.02154i	0.301406	−	0.215468i
$782$	7.80943	−	1.56963i	0.279265	−	0.0561299i
$783$	−4.62399	−	2.96027i	−0.165248	−	0.105791i
$784$	−2.64094	+	4.09627i	−0.0943192	+	0.146295i
$785$	−4.78487	+	0.771977i	−0.170779	+	0.0275531i
$786$	−5.67715	+	1.52443i	−0.202497	+	0.0543747i
$787$	2.67797	+	36.3291i	0.0954594	+	1.29499i	0.806243	+	0.591584i	$0.201497\pi$
$787$	2.67797	+	36.3291i	0.0954594	+	1.29499i	−0.710784	+	0.703410i	$0.751660\pi$
$788$	−35.4153	−	14.3058i	−1.26162	−	0.509623i
$789$	−1.28718	+	4.61623i	−0.0458247	+	0.164342i
$790$	−22.4584	−	21.4057i	−0.799035	−	0.761582i
$791$	24.9225	−	20.6123i	0.886142	−	0.732890i
$792$	37.3871	+	19.7633i	1.32849	+	0.702258i
$793$	0.103411	+	10.7744i	0.00367224	+	0.382611i
$794$	13.5017	+	5.55468i	0.479158	+	0.197128i
$795$	0.121110	−	0.326593i	0.00429533	−	0.0115831i
$796$	90.5638	−	33.2545i	3.20995	−	1.17867i
$797$	−14.8488	−	3.68316i	−0.525971	−	0.130464i	−0.0312422	−	0.999512i	$-0.509946\pi$
$797$	−14.8488	−	3.68316i	−0.525971	−	0.130464i	−0.494728	+	0.869048i	$0.664732\pi$
$798$	0.403623	−	1.13269i	0.0142881	−	0.0400968i
$799$	3.38645	+	3.96374i	0.119804	+	0.140227i
$800$	−5.95274	−	16.0525i	−0.210461	−	0.567543i
$801$	−0.279066	+	7.92679i	−0.00986033	+	0.280079i
$802$	34.2517	+	68.4635i	1.20947	+	2.41753i
$803$	8.49868	+	6.93780i	0.299912	+	0.244830i
$804$	3.58957	+	1.72461i	0.126594	+	0.0608222i
$805$	7.15125	−	5.61259i	0.252048	−	0.197818i
$806$	−105.960	−	70.7392i	−3.73229	−	2.49168i
$807$	−0.849216	−	3.90105i	−0.0298938	−	0.137324i
$808$	5.85726	+	0.149940i	0.206058	+	0.00527487i
$809$	3.11492	+	23.6115i	0.109515	+	0.830136i	0.955097	+	0.296292i	$0.0957501\pi$
$809$	3.11492	+	23.6115i	0.109515	+	0.830136i	−0.845583	+	0.533844i	$0.820747\pi$
$810$	26.7802	−	5.02695i	0.940960	−	0.176629i
$811$	−0.850725	+	53.1794i	−0.0298730	+	1.86738i	0.342785	+	0.939414i	$0.388630\pi$
$811$	−0.850725	+	53.1794i	−0.0298730	+	1.86738i	−0.372658	+	0.927969i	$0.621553\pi$
$812$	6.12743	−	57.8240i	0.215031	−	2.02923i
$813$	1.64233	+	0.881647i	0.0575990	+	0.0309207i
$814$	1.05609	−	7.28509i	0.0370159	−	0.255342i
$815$	−0.0950710	+	0.272296i	−0.00333019	+	0.00953812i
$816$	−0.231633	−	1.25614i	−0.00810879	−	0.0439735i
$817$	−0.143612	+	6.41182i	−0.00502435	+	0.224321i
$818$	64.2932	−	27.9052i	2.24796	−	0.975683i
$819$	−31.4827	−	28.5056i	−1.10009	−	0.996066i
$820$	−45.0987	+	11.4933i	−1.57492	+	0.401364i
$821$	1.68817	+	1.73749i	0.0589175	+	0.0606388i	0.746030	−	0.665912i	$-0.231957\pi$
$821$	1.68817	+	1.73749i	0.0589175	+	0.0606388i	−0.687113	+	0.726551i	$0.741122\pi$
$822$	−6.26002	−	2.07393i	−0.218343	−	0.0723367i
$823$	20.6843	−	28.3549i	0.721010	−	0.988390i	−0.278598	−	0.960408i	$-0.589870\pi$
$823$	20.6843	−	28.3549i	0.721010	−	0.988390i	0.999608	−	0.0279824i	$-0.00890823\pi$
$824$	−2.31785	+	0.543543i	−0.0807461	+	0.0189352i
$825$	−0.247210	+	1.39043i	−0.00860673	+	0.0484086i
$826$	36.0833	+	39.0911i	1.25550	+	1.36015i
$827$	−0.867083	+	1.81962i	−0.0301514	+	0.0632745i	−0.917267	−	0.398273i	$-0.869610\pi$
$827$	−0.867083	+	1.81962i	−0.0301514	+	0.0632745i	0.887116	+	0.461547i	$0.152706\pi$
$828$	38.7934	−	0.248218i	1.34816	−	0.00862616i
$829$	−18.4009	−	19.4299i	−0.639089	−	0.674827i	0.323364	−	0.946274i	$-0.395186\pi$
$829$	−18.4009	−	19.4299i	−0.639089	−	0.674827i	−0.962453	+	0.271448i	$0.912498\pi$
$830$	7.78017	+	5.41277i	0.270054	+	0.187880i
$831$	1.06814	+	0.0547223i	0.0370532	+	0.00189830i
$832$	−6.18834	+	2.22749i	−0.214542	+	0.0772244i
$833$	0.691872	+	0.321578i	0.0239719	+	0.0111420i
$834$	−1.17457	−	4.54808i	−0.0406722	−	0.157487i
$835$	−11.0008	−	4.69126i	−0.380698	−	0.162348i
$836$	2.26795	+	10.7487i	0.0784387	+	0.371753i
$837$	−7.48387	+	5.42273i	−0.258680	+	0.187437i
$838$	36.4379	+	91.0430i	1.25873	+	3.14503i
$839$	12.2241	−	13.2431i	0.422023	−	0.457202i	−0.487335	−	0.873215i	$-0.662031\pi$
$839$	12.2241	−	13.2431i	0.422023	−	0.457202i	0.909359	+	0.416013i	$0.136573\pi$
$840$	−2.03012	−	2.67364i	−0.0700460	−	0.0922495i
$841$	0.589173	+	1.55815i	0.0203163	+	0.0537292i
$842$	6.09951	−	27.1814i	0.210203	−	0.936733i
$843$	0.0757682	−	0.874989i	0.00260959	−	0.0301362i
$844$	−22.8265	+	43.5182i	−0.785719	+	1.49796i
$845$	−17.9561	−	16.0502i	−0.617708	−	0.552145i
$846$	18.1452	+	32.0570i	0.623846	+	1.10214i
$847$	−7.49912	+	12.1370i	−0.257673	+	0.417032i
$848$	9.33401	+	5.72605i	0.320531	+	0.196633i
$849$	−1.58826	−	3.89594i	−0.0545089	−	0.133708i
$850$	−8.30216	+	4.45682i	−0.284762	+	0.152868i
$851$	−1.26721	−	3.48549i	−0.0434394	−	0.119481i
$852$	−3.12173	−	1.59942i	−0.106949	−	0.0547951i
$853$	−0.619764	+	3.13542i	−0.0212203	+	0.107355i	−0.990159	−	0.139946i	$-0.955307\pi$
$853$	−0.619764	+	3.13542i	−0.0212203	+	0.107355i	0.968939	+	0.247300i	$0.0795434\pi$
$854$	1.41827	+	11.9257i	0.0485323	+	0.408089i
$855$	3.02746	+	2.50388i	0.103537	+	0.0856308i
$856$	−9.15942	−	22.0629i	−0.313063	−	0.754093i
$857$	−7.69297	+	37.6511i	−0.262787	+	1.28614i	0.607787	+	0.794100i	$0.292057\pi$
$857$	−7.69297	+	37.6511i	−0.262787	+	1.28614i	−0.870574	+	0.492038i	$0.836252\pi$
$858$	−5.76758	−	1.08264i	−0.196902	−	0.0369608i
$859$	2.42261	−	44.5008i	0.0826585	−	1.51835i	−0.607284	−	0.794485i	$-0.707741\pi$
$859$	2.42261	−	44.5008i	0.0826585	−	1.51835i	0.689942	−	0.723864i	$-0.257636\pi$
$860$	26.8810	+	18.4474i	0.916635	+	0.629051i
$861$	3.21525	−	1.94423i	0.109575	−	0.0662591i
$862$	27.6877	+	3.56258i	0.943045	+	0.121342i
$863$	−23.3447	+	43.1545i	−0.794662	+	1.46900i	0.0865359	+	0.996249i	$0.472420\pi$
$863$	−23.3447	+	43.1545i	−0.794662	+	1.46900i	−0.881198	+	0.472748i	$0.843262\pi$
$864$	0.0495297	−	5.16051i	0.00168503	−	0.175564i
$865$	−5.80412	+	13.7320i	−0.197346	+	0.466901i
$866$	17.2066	−	53.6564i	0.584703	−	1.82332i
$867$	2.64929	−	0.877705i	0.0899747	−	0.0298084i
$868$	−86.8247	−	45.1883i	−2.94702	−	1.53379i
$869$	−22.8044	+	1.90123i	−0.773586	+	0.0644947i
$870$	−2.58197	−	1.26090i	−0.0875370	−	0.0427486i
$871$	28.7981	+	4.26886i	0.975788	+	0.144645i
$872$	78.1603	+	21.5248i	2.64684	+	0.728920i
$873$	−4.14135	−	6.07623i	−0.140163	−	0.205649i
$874$	5.17660	+	6.13815i	0.175101	+	0.207626i
$875$	−15.0243	+	21.4488i	−0.507914	+	0.725102i
$876$	0.767282	−	3.63646i	0.0259240	−	0.122865i
$877$	−21.7221	−	48.7607i	−0.733504	−	1.64653i	−0.762529	−	0.646954i	$-0.776043\pi$
$877$	−21.7221	−	48.7607i	−0.733504	−	1.64653i	0.0290251	−	0.999579i	$-0.490760\pi$
$878$	1.92559	+	40.0960i	0.0649856	+	1.35317i
$879$	1.25950	+	0.329577i	0.0424820	+	0.0111164i
$880$	18.0058	+	7.00669i	0.606977	+	0.236196i
$881$	−9.32659	+	20.9358i	−0.314221	+	0.705347i	−0.999742	−	0.0227059i	$-0.992772\pi$
$881$	−9.32659	+	20.9358i	−0.314221	+	0.705347i	0.685521	+	0.728052i	$0.259574\pi$
$882$	4.36530	+	3.16305i	0.146987	+	0.106505i
$883$	−8.36321	+	33.2608i	−0.281445	+	1.11932i	0.651312	+	0.758810i	$0.274219\pi$
$883$	−8.36321	+	33.2608i	−0.281445	+	1.11932i	−0.932757	+	0.360506i	$0.882604\pi$
$884$	−12.5363	−	23.9003i	−0.421642	−	0.803853i
$885$	1.67129	−	0.700115i	0.0561799	−	0.0235341i
$886$	−53.6351	+	2.74781i	−1.80191	+	0.0923145i
$887$	5.17440	+	3.22004i	0.173739	+	0.108118i	0.612448	−	0.790511i	$-0.290185\pi$
$887$	5.17440	+	3.22004i	0.173739	+	0.108118i	−0.438708	+	0.898630i	$0.644564\pi$
$888$	−1.29445	+	0.447311i	−0.0434389	+	0.0150108i
$889$	43.2874	+	1.38531i	1.45181	+	0.0464619i
$890$	0.666749	+	8.31872i	0.0223495	+	0.278844i
$891$	10.3441	−	17.2307i	0.346540	−	0.577251i
$892$	60.5482	−	17.9317i	2.02730	−	0.600397i
$893$	−1.85870	+	4.91557i	−0.0621990	+	0.164493i
$894$	7.08424	+	4.66419i	0.236933	+	0.155994i
$895$	−12.2998	+	7.33047i	−0.411136	+	0.245031i
$896$	−28.7272	+	14.0289i	−0.959707	+	0.468672i
$897$	−2.81820	+	0.893809i	−0.0940969	+	0.0298434i
$898$	−10.6087	+	61.9665i	−0.354016	+	2.06785i
$899$	−46.0078	−	0.588781i	−1.53445	−	0.0196370i
$900$	−43.8316	+	13.5934i	−1.46105	+	0.453114i
$901$	0.687527	−	1.57028i	0.0229048	−	0.0523135i
$902$	−22.8501	+	44.2493i	−0.760827	+	1.47334i
$903$	−2.50893	−	0.795723i	−0.0834920	−	0.0264800i
$904$	78.8912	−	11.6943i	2.62388	−	0.388948i
$905$	12.4552	+	1.52166i	0.414024	+	0.0505818i
$906$	0.124294	−	0.233323i	0.00412940	−	0.00775164i
$907$	−6.34483	−	22.7546i	−0.210676	−	0.755554i	−0.991421	−	0.130704i	$-0.958276\pi$
$907$	−6.34483	−	22.7546i	−0.210676	−	0.755554i	0.780745	−	0.624850i	$-0.214840\pi$
$908$	3.39218	−	30.1684i	0.112573	−	1.00117i
$909$	0.224831	−	2.80512i	0.00745719	−	0.0930399i
$910$	−36.3519	−	25.9871i	−1.20505	−	0.861464i
$911$	−45.2744	−	20.3429i	−1.50001	−	0.673989i	−0.516738	−	0.856144i	$-0.672854\pi$
$911$	−45.2744	−	20.3429i	−1.50001	−	0.673989i	−0.983270	+	0.182154i	$0.941693\pi$
$912$	0.997427	−	0.814237i	0.0330281	−	0.0269621i
$913$	6.79557	−	1.63952i	0.224901	−	0.0542603i
$914$	18.6933	−	43.4491i	0.618320	−	1.43717i
$915$	0.398260	+	0.0933932i	0.0131661	+	0.00308748i
$916$	−70.4924	+	60.6169i	−2.32914	+	2.00284i
$917$	−25.8399	+	20.5488i	−0.853310	+	0.678580i
$918$	−2.81711	+	0.362479i	−0.0929786	+	0.0119636i
$919$	16.5747	−	43.0002i	0.546748	−	1.41845i	−0.332964	−	0.942940i	$-0.608049\pi$
$919$	16.5747	−	43.0002i	0.546748	−	1.41845i	0.879712	−	0.475507i	$-0.157736\pi$
$920$	22.2518	−	2.71853i	0.733619	−	0.0896271i
$921$	1.99662	−	0.549855i	0.0657910	−	0.0181183i
$922$	−40.1635	−	34.0923i	−1.32272	−	1.12277i
$923$	−25.2604	−	4.40781i	−0.831456	−	0.145085i
$924$	−4.49516	−	0.345820i	−0.147880	−	0.0113766i
$925$	2.63065	+	3.51095i	0.0864954	+	0.115439i
$926$	22.6703	+	52.6929i	0.744991	+	1.73160i
$927$	0.200158	+	1.12579i	0.00657404	+	0.0369757i
$928$	15.5374	−	20.4626i	0.510042	−	0.671717i
$929$	51.1750	+	15.1558i	1.67900	+	0.497244i	0.976694	−	0.214634i	$-0.0688560\pi$
$929$	51.1750	+	15.1558i	1.67900	+	0.497244i	0.702302	+	0.711879i	$0.252155\pi$
$930$	−3.56461	+	3.26928i	−0.116888	+	0.107204i
$931$	0.0516302	+	0.767347i	0.00169211	+	0.0251488i
$932$	51.1286	+	4.92221i	1.67477	+	0.161232i
$933$	−0.952571	+	0.0732827i	−0.0311858	+	0.00239917i
$934$	23.0179	+	26.2539i	0.753168	+	0.859055i
$935$	0.699951	−	2.94245i	0.0228908	−	0.0962283i
$936$	−30.0605	−	100.322i	−0.982557	−	3.27914i
$937$	32.6190	+	7.21017i	1.06562	+	0.235546i	0.713675	−	0.700477i	$-0.247029\pi$
$937$	32.6190	+	7.21017i	1.06562	+	0.235546i	0.351940	+	0.936023i	$0.385522\pi$
$938$	32.4253	+	1.24542i	1.05872	+	0.0406645i
$939$	4.09526	+	3.52155i	0.133644	+	0.114921i
$940$	15.7439	+	21.5823i	0.513509	+	0.703939i
$941$	−1.63140	−	5.08729i	−0.0531820	−	0.165841i	0.922028	−	0.387124i	$-0.126531\pi$
$941$	−1.63140	−	5.08729i	−0.0531820	−	0.165841i	−0.975210	+	0.221283i	$0.928975\pi$
$942$	1.74989	+	0.157170i	0.0570143	+	0.00512088i
$943$	0.401327	+	25.0872i	0.0130690	+	0.816952i
$944$	11.4036	+	55.8116i	0.371154	+	1.81651i
$945$	−2.68438	+	1.81703i	−0.0873230	+	0.0591081i
$946$	33.8602	−	8.39884i	1.10089	−	0.273070i
$947$	−1.46579	+	14.7314i	−0.0476318	+	0.478707i	0.942055	+	0.335458i	$0.108891\pi$
$947$	−1.46579	+	14.7314i	−0.0476318	+	0.478707i	−0.989687	+	0.143248i	$0.954245\pi$
$948$	4.11685	+	6.56858i	0.133709	+	0.213338i
$949$	−2.51706	−	27.0525i	−0.0817071	−	0.878162i
$950$	−7.96664	−	5.17239i	−0.258472	−	0.167815i
$951$	−1.64173	−	0.0735796i	−0.0532366	−	0.00238598i
$952$	−9.21692	−	13.7109i	−0.298722	−	0.444372i
$953$	4.81526	+	31.7829i	0.155981	+	1.02955i	0.922129	+	0.386883i	$0.126448\pi$
$953$	4.81526	+	31.7829i	0.155981	+	1.02955i	−0.766147	+	0.642665i	$0.777829\pi$
$954$	6.88529	−	9.96457i	0.222919	−	0.322615i
$955$	−12.9943	+	7.08319i	−0.420487	+	0.229207i
$956$	−4.34607	−	123.449i	−0.140562	−	3.99261i
$957$	−1.95995	+	0.806334i	−0.0633562	+	0.0260651i
$958$	−14.7805	−	34.9691i	−0.477535	−	1.12980i
$959$	−36.8893	+	3.31330i	−1.19122	+	0.106992i
$960$	0.0263119	+	0.248303i	0.000849213	+	0.00801395i
$961$	−17.5356	+	43.0142i	−0.565665	+	1.38756i
$962$	−14.6934	+	10.7907i	−0.473734	+	0.347907i
$963$	−10.8201	+	3.81666i	−0.348672	+	0.122990i
$964$	43.7704	+	33.4566i	1.40975	+	1.07756i
$965$	−30.9570	+	7.05084i	−0.996540	+	0.226975i
$966$	−3.01445	+	1.33135i	−0.0969885	+	0.0428355i
$967$	−4.57781	−	16.0206i	−0.147212	−	0.515187i	0.852762	−	0.522299i	$-0.174926\pi$
$967$	−4.57781	−	16.0206i	−0.147212	−	0.515187i	−0.999975	+	0.00711211i	$0.997736\pi$
$968$	−31.3109	+	16.0421i	−1.00637	+	0.515613i
$969$	−0.147670	−	0.137185i	−0.00474383	−	0.00440701i
$970$	−5.06316	−	5.85007i	−0.162568	−	0.187834i
$971$	−1.41897	−	3.24086i	−0.0455370	−	0.104004i	0.891798	−	0.452434i	$-0.149444\pi$
$971$	−1.41897	−	3.24086i	−0.0455370	−	0.104004i	−0.937335	+	0.348430i	$0.886715\pi$
$972$	−20.7429	−	1.32902i	−0.665330	−	0.0426283i
$973$	−16.2215	−	20.8053i	−0.520039	−	0.666986i
$974$	−8.48735	−	13.9350i	−0.271952	−	0.446507i
$975$	2.88367	−	1.97895i	0.0923513	−	0.0633771i
$976$	−5.30814	+	11.7132i	−0.169909	+	0.374932i
$977$	−18.5184	+	16.7672i	−0.592456	+	0.536432i	−0.911496	−	0.411310i	$-0.865071\pi$
$977$	−18.5184	+	16.7672i	−0.592456	+	0.536432i	0.319040	+	0.947741i	$0.396640\pi$
$978$	0.0577716	−	0.0871385i	0.00184733	−	0.00278638i
$979$	4.91414	+	3.70663i	0.157056	+	0.118464i
$980$	3.40847	+	1.91493i	0.108880	+	0.0611701i
$981$	12.3635	−	36.9223i	0.394736	−	1.17884i
$982$	−91.7606			−2.92820
$983$	15.7768	+	27.0941i	0.503203	+	0.864168i
$983$	15.7768	+	27.0941i	0.503203	+	0.864168i
$984$	9.26546			0.295372
$985$	−3.36596	+	10.0521i	−0.107248	+	0.320286i
$986$	−12.3283	−	6.92624i	−0.392614	−	0.220576i
$987$	−1.72187	−	1.29877i	−0.0548078	−	0.0413404i
$988$	15.0329	−	22.6746i	0.478262	−	0.721376i
$989$	13.0290	−	11.7969i	0.414298	−	0.375121i
$990$	8.82108	−	19.4651i	0.280352	−	0.618641i
$991$	−10.2373	+	7.02543i	−0.325197	+	0.223170i	−0.717322	−	0.696742i	$-0.754632\pi$
$991$	−10.2373	+	7.02543i	−0.325197	+	0.223170i	0.392125	+	0.919912i	$0.371740\pi$
$992$	−22.4972	−	36.9371i	−0.714286	−	1.17275i
$993$	1.83963	+	2.35945i	0.0583788	+	0.0748750i
$994$	−28.5222	−	1.82745i	−0.904670	−	0.0579632i
$995$	−10.7391	−	24.5276i	−0.340453	−	0.777579i
$996$	−1.54976	−	1.79062i	−0.0491060	−	0.0567380i
$997$	−36.4806	−	33.8905i	−1.15535	−	1.07332i	−0.996290	−	0.0860539i	$-0.972574\pi$
$997$	−36.4806	−	33.8905i	−1.15535	−	1.07332i	−0.159063	−	0.987268i	$-0.550847\pi$
$998$	43.6323	−	22.3550i	1.38116	−	0.707635i
$999$	0.363336	+	1.27154i	0.0114955	+	0.0402297i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.c.a.2.6	✓	39690
983.492	even	491	inner	983.2.c.a.492.6	yes	39690

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.c.a.2.6	✓	39690	1.1	even	1	trivial
983.2.c.a.492.6	yes	39690	983.492	even	491	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.c (of order \(491\), degree \(490\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.805572 + 2.40575i) q^{2} +(-0.153383 - 0.0861729i) q^{3} +(-3.54199 - 2.67165i) q^{4} +(-0.680394 + 1.02626i) q^{5} +(0.330872 - 0.299584i) q^{6} +(1.03475 - 2.28334i) q^{7} +(5.09698 - 3.49786i) q^{8} +(-1.54443 - 2.53574i) q^{9} +O(q^{10})\)	\(q+(-0.805572 + 2.40575i) q^{2} +(-0.153383 - 0.0861729i) q^{3} +(-3.54199 - 2.67165i) q^{4} +(-0.680394 + 1.02626i) q^{5} +(0.330872 - 0.299584i) q^{6} +(1.03475 - 2.28334i) q^{7} +(5.09698 - 3.49786i) q^{8} +(-1.54443 - 2.53574i) q^{9} +(-1.92082 - 2.46358i) q^{10} +(-2.29938 - 0.147324i) q^{11} +(0.313059 + 0.715010i) q^{12} +(3.73418 + 4.31455i) q^{13} +(4.65958 + 4.32875i) q^{14} +(0.192797 - 0.0987793i) q^{15} +(1.87110 + 6.54813i) q^{16} +(0.975206 - 0.430705i) q^{17} +(7.34452 - 1.67281i) q^{18} +(0.853792 + 0.652610i) q^{19} +(5.15175 - 1.81722i) q^{20} +(-0.355475 + 0.261058i) q^{21} +(2.20674 - 5.41307i) q^{22} +(-0.310345 - 2.92870i) q^{23} +(-1.08321 + 0.0972912i) q^{24} +(1.35635 + 3.20899i) q^{25} +(-13.3879 + 5.50785i) q^{26} +(0.0369481 + 1.04950i) q^{27} +(-9.76535 + 5.32307i) q^{28} +(-2.97208 + 4.30127i) q^{29} +(0.0823270 + 0.543395i) q^{30} +(4.90984 + 7.30375i) q^{31} +(-4.90937 - 0.220030i) q^{32} +(0.339992 + 0.220742i) q^{33} +(0.250572 + 2.69307i) q^{34} +(1.63926 + 2.61549i) q^{35} +(-1.30423 + 13.1077i) q^{36} +(1.22224 - 0.303170i) q^{37} +(-2.25781 + 1.52829i) q^{38} +(-0.200964 - 0.983565i) q^{39} +(0.121751 + 7.61073i) q^{40} +(-8.48523 - 0.762121i) q^{41} +(-0.341681 - 1.06549i) q^{42} +(3.51714 + 4.82143i) q^{43} +(7.75080 + 6.66496i) q^{44} +(3.65314 + 0.140314i) q^{45} +(7.29574 + 1.61267i) q^{46} +(1.40364 + 4.68444i) q^{47} +(0.277276 - 1.16561i) q^{48} +(0.471797 + 0.538126i) q^{49} +(-8.81267 + 0.677972i) q^{50} +(-0.186695 - 0.0179734i) q^{51} +(-1.69949 - 25.2585i) q^{52} +(1.18501 - 1.08683i) q^{53} +(-2.55460 - 0.756559i) q^{54} +(1.71568 - 2.25952i) q^{55} +(-2.71269 - 15.2575i) q^{56} +(-0.0747202 - 0.173673i) q^{57} +(-7.95357 - 10.6151i) q^{58} +(8.33995 + 0.641605i) q^{59} +(-0.946788 - 0.165210i) q^{60} +(1.43961 + 1.22200i) q^{61} +(-21.5263 + 5.92817i) q^{62} +(-7.38805 + 0.902607i) q^{63} +(-0.414558 + 1.07550i) q^{64} +(-6.96855 + 0.896645i) q^{65} +(-0.804938 + 0.640113i) q^{66} +(3.86849 - 3.32654i) q^{67} +(-4.60486 - 1.07985i) q^{68} +(-0.204773 + 0.475957i) q^{69} +(-7.61276 + 1.83668i) q^{70} +(-3.48116 + 2.84181i) q^{71} +(-16.7416 - 7.52240i) q^{72} +(-3.87349 - 2.76907i) q^{73} +(-0.255250 + 3.18464i) q^{74} +(0.0684865 - 0.609086i) q^{75} +(-1.28058 - 4.59257i) q^{76} +(-2.71568 + 5.09782i) q^{77} +(2.52811 + 0.308862i) q^{78} +(9.82431 - 1.45630i) q^{79} +(-7.99315 - 2.53508i) q^{80} +(-4.00209 + 7.75005i) q^{81} +(8.66894 - 19.7994i) q^{82} +(-2.89781 + 0.898693i) q^{83} +(1.95655 + 0.0250387i) q^{84} +(-0.221509 + 1.29386i) q^{85} +(-14.4325 + 4.57735i) q^{86} +(0.826521 - 0.403630i) q^{87} +(-12.2352 + 7.29200i) q^{88} +(-2.23128 - 1.46905i) q^{89} +(-3.28043 + 8.67553i) q^{90} +(13.7155 - 4.06192i) q^{91} +(-6.72522 + 11.2026i) q^{92} +(-0.123702 - 1.54337i) q^{93} +(-12.4004 - 0.396845i) q^{94} +(-1.25066 + 0.432179i) q^{95} +(0.734055 + 0.456804i) q^{96} +(2.47342 - 0.126717i) q^{97} +(-1.67466 + 0.701528i) q^{98} +(3.17767 + 6.05816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9}+O(q^{10}) \) 39690 * q - 489 * q^2 - 487 * q^3 - 565 * q^4 - 485 * q^5 - 477 * q^6 - 489 * q^7 - 485 * q^8 - 558 * q^9	\( 39690 q - 489 q^{2} - 487 q^{3} - 565 q^{4} - 485 q^{5} - 477 q^{6} - 489 q^{7} - 485 q^{8} - 558 q^{9} - 471 q^{10} - 477 q^{11} - 463 q^{12} - 483 q^{13} - 473 q^{14} - 461 q^{15} - 543 q^{16} - 481 q^{17} - 457 q^{18} - 473 q^{19} - 449 q^{20} - 449 q^{21} - 459 q^{22} - 473 q^{23} - 405 q^{24} - 552 q^{25} - 437 q^{26} - 451 q^{27} - 455 q^{28} - 455 q^{29} - 379 q^{30} - 459 q^{31} - 437 q^{32} - 447 q^{33} - 423 q^{34} - 439 q^{35} - 459 q^{36} - 475 q^{37} - 423 q^{38} - 439 q^{39} - 413 q^{40} - 455 q^{41} - 407 q^{42} - 457 q^{43} - 413 q^{44} - 397 q^{45} - 415 q^{46} - 467 q^{47} - 393 q^{48} - 524 q^{49} - 429 q^{50} - 403 q^{51} - 391 q^{52} - 431 q^{53} - 379 q^{54} - 415 q^{55} - 371 q^{56} - 447 q^{57} - 431 q^{58} - 439 q^{59} - 261 q^{60} - 431 q^{61} - 383 q^{62} - 445 q^{63} - 447 q^{64} - 415 q^{65} - 345 q^{66} - 439 q^{67} - 409 q^{68} - 367 q^{69} - 345 q^{70} - 415 q^{71} - 341 q^{72} - 465 q^{73} - 359 q^{74} - 339 q^{75} - 361 q^{76} - 363 q^{77} - 341 q^{78} - 423 q^{79} - 249 q^{80} - 420 q^{81} - 371 q^{82} - 433 q^{83} - 215 q^{84} - 409 q^{85} - 369 q^{86} - 329 q^{87} - 255 q^{88} - 393 q^{89} - 251 q^{90} - 373 q^{91} - 387 q^{92} - 369 q^{93} - 317 q^{94} - 393 q^{95} - 149 q^{96} - 415 q^{97} - 307 q^{98} - 299 q^{99}+O(q^{100}) \) 39690 * q - 489 * q^2 - 487 * q^3 - 565 * q^4 - 485 * q^5 - 477 * q^6 - 489 * q^7 - 485 * q^8 - 558 * q^9 - 471 * q^10 - 477 * q^11 - 463 * q^12 - 483 * q^13 - 473 * q^14 - 461 * q^15 - 543 * q^16 - 481 * q^17 - 457 * q^18 - 473 * q^19 - 449 * q^20 - 449 * q^21 - 459 * q^22 - 473 * q^23 - 405 * q^24 - 552 * q^25 - 437 * q^26 - 451 * q^27 - 455 * q^28 - 455 * q^29 - 379 * q^30 - 459 * q^31 - 437 * q^32 - 447 * q^33 - 423 * q^34 - 439 * q^35 - 459 * q^36 - 475 * q^37 - 423 * q^38 - 439 * q^39 - 413 * q^40 - 455 * q^41 - 407 * q^42 - 457 * q^43 - 413 * q^44 - 397 * q^45 - 415 * q^46 - 467 * q^47 - 393 * q^48 - 524 * q^49 - 429 * q^50 - 403 * q^51 - 391 * q^52 - 431 * q^53 - 379 * q^54 - 415 * q^55 - 371 * q^56 - 447 * q^57 - 431 * q^58 - 439 * q^59 - 261 * q^60 - 431 * q^61 - 383 * q^62 - 445 * q^63 - 447 * q^64 - 415 * q^65 - 345 * q^66 - 439 * q^67 - 409 * q^68 - 367 * q^69 - 345 * q^70 - 415 * q^71 - 341 * q^72 - 465 * q^73 - 359 * q^74 - 339 * q^75 - 361 * q^76 - 363 * q^77 - 341 * q^78 - 423 * q^79 - 249 * q^80 - 420 * q^81 - 371 * q^82 - 433 * q^83 - 215 * q^84 - 409 * q^85 - 369 * q^86 - 329 * q^87 - 255 * q^88 - 393 * q^89 - 251 * q^90 - 373 * q^91 - 387 * q^92 - 369 * q^93 - 317 * q^94 - 393 * q^95 - 149 * q^96 - 415 * q^97 - 307 * q^98 - 299 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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